0. Review of Algebra

Radical Expressions

0. Review of Algebra

# Radical Expressions - Video Tutorials & Practice Problems

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concept

## Square Roots

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2

Problem

ProblemEvaluate the radical. $-\sqrt{\frac14}$

A

$\frac12$

B

$-\frac12$

C

$-\frac{1}{16}$

D

No real solution (Imaginary)

3

Problem

ProblemEvaluate the radical. $\sqrt{\left(-5\right)^2}$

A

$2.23$

B

$5$

C

$-5$

D

No real solution (Imaginary)

4

concept

## Nth Roots

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PRACTICE PROBLEMS AND ACTIVITIES (389)

- In Exercises 1–14, multiply using the product rule. b⁴•b⁷
- Write ∛64 using exponents and evaluate.
- In this Exercise Set, assume that all variables represent positive real numbers. In Exercises 1–10, add or sub...
- Determine whether each statement is true or false. If false, correct the right side of the equation. (y^2)(y^5...
- Write 27^2/3 in radical form and evaluate.
- In Exercises 1–14, multiply using the product rule. x•x³
- Match the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume...
- Evaluate each exponential expression in Exercises 1–22. (−2)^6
- Match the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume...
- Match the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume...
- In Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (-27)^⅓
- In Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ___ -√ 36
- In Exercises 4–6, evaluate each algebraic expression for the given value or values of the variable. 6+2(x-8)³...
- In Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. -16^¼
- In Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ___ √-36
- Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √−25
- In Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the pro...
- In Exercises 1–20, use the product rule to multiply. _ _ ⁴√9 ⋅ ⁴√3
- In Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (xy)^⅓
- In Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ____ √1/25
- Perform the operation and/or simplify each of the following. Assume all variables represent positive real numb...
- Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √144+25
- In Exercises 1–20, use the product rule to multiply. __ ___ √5x ⋅ √11y
- Determine whether each statement is true or false. If false, correct the right side of the equation. (m^2/3)(m...
- In Exercises 1–38, solve each radical equation. _____ x = √6x + 7
- In Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the pro...
- In Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (2xy³)^⅕
- In Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ____ -√9/16
- Perform the operation and/or simplify each of the following. Assume all variables represent positive real numb...
- Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √25−√16
- Perform the operation and/or simplify each of the following. Assume all variables represent positive real numb...
- In Exercises 1–20, use the product rule to multiply. ___ __ ⁴√6x² ⋅ ⁴√3x
- Match each expression in Column I with its equivalent expression in Column II. Choices may be used once, more ...
- In Exercises 1–38, solve each radical equation. _____ √2x + 1 = x - 7
- In Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the pro...
- Rewrite each expression without the absolute value bars. |√2-1|
- In this Exercise Set, assume that all variables represent positive real numbers. In Exercises 1–10, add or sub...
- In Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. 81^3/2
- In Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ____ √0.81
- Write each root using exponents and evaluate. ∛125
- Evaluate each exponential expression in Exercises 1–22. 4^−3
- In Exercises 1–14, multiply using the product rule. (5x³y⁴)(20x⁷y⁸)
- Write each root using exponents and evaluate. ∛216
- Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √(−17)^2
- In Exercises 1–20, use the product rule to multiply. ___ ___ √x+6 ⋅ √x-6
- Simplify each expression. See Example 1. (3y^4)(-6y^3)
- In Exercises 1–38, solve each radical equation. _____ x = √3x + 7 - 3
- In Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radical...
- Simplify each expression. See Example 1. (n^6)(n^4)(n)
- Evaluate each exponential expression in Exercises 1–22. 2^2⋅2^3
- In Exercises 1–14, multiply using the product rule. (-3x⁴y⁰z)(-7xyz³)
- Simplify each expression. See Example 1. (a^8)(a^5)(a)
- In Exercises 1–20, use the product rule to multiply. ___ _____ ⁶√x-5 ⋅ ⁶√(x-5)⁴
- In Exercises 1–38, solve each radical equation. _____ 3x - √3x + 7 = -5
- In Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radical...
- Write each root using exponents and evaluate. ∜256
- Write each root using exponents and evaluate. ∛-125
- In Exercises 1–38, solve each radical equation. _____ _____ √6x + 2 = √5x + 3
- In Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radical...
- Evaluate each exponential expression in Exercises 1–22. (3^3)^2
- Write each root using exponents and evaluate. ∛-343
- Write each root using exponents and evaluate. ∜-81
- In Exercises 15–24, divide using the quotient rule. 15x⁹/3x⁴
- Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables...
- Write each root using exponents and evaluate. ∜-256
- Evaluate each exponential expression in Exercises 1–22. 3^8/3^4
- Write each root using exponents and evaluate. ⁵√32
- In Exercises 15–24, divide using the quotient rule. x⁹y⁷/x⁴y²
- Simplify each expression. See Example 1. (5x^2y)(-3x^3y^4)
- In Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (xy)^4/7
- In Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ______ √16 − 2...
- Evaluate each exponential expression in Exercises 1–22. 2^3/2^7
- In Exercises 15–24, divide using the quotient rule. 50x²y⁷/5xy⁴
- In Exercises 21–38, rewrite each expression with rational exponents. _ √7
- Write each root using exponents and evaluate. - ∛-343
- Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables...
- Simplify each expression. See Example 1. (35m^4n)(-2/7mn^2)
- In Exercises 21–32, simplify by factoring. __ √27
- Simplify each exponential expression in Exercises 23–64. x^−2y
- In Exercises 15–24, divide using the quotient rule. -56a^12b^10c^8/7ab^2c^4
- In Exercises 21–38, rewrite each expression with rational exponents. _ ∛5
- In Exercises 21–32, simplify by factoring. __ √28
- In Exercises 1–38, solve each radical equation. ____ ____ √x - 4 + √x + 4 = 4
- Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (6^4)^3
- In Exercises 25–34, use the zero-exponent rule to simplify each expression. 6⁰
- In Exercises 21–38, rewrite each expression with rational exponents. ___ ⁵√11x
- In Exercises 21–32, simplify by factoring. ___ √40x
- In Exercises 1–38, solve each radical equation. ____ 2√x - 3 + 4 = x + 1
- Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (-2x^5)^5
- If the expression is in exponential form, write it in radical form and evaluate if possible. If it is in radic...
- In Exercises 21–38, rewrite each expression with rational exponents. __ √x³
- In Exercises 21–32, simplify by factoring. __ ³√54
- In Exercises 1–38, solve each radical equation. (3x - 6)¹/³ + 5 = 8
- Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. -(2x^0y^4)^3
- If the expression is in exponential form, write it in radical form and evaluate if possible. If it is in radic...
- Simplify each exponential expression in Exercises 23–64. x^−5⋅x^10
- In Exercises 21–32, simplify by factoring. _____ ³√250x³
- In Exercises 1–38, solve each radical equation. (2x + 3)¹/⁴ + 7 = 10
- Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (p^4/q)^2
- In Exercises 29–44, simplify using the quotient rule. _____ √19/25
- If the expression is in exponential form, write it in radical form and evaluate if possible. If it is in radic...
- Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. √24x^4/√3x
- Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (-5n^4/r^2)^3
- In Exercises 29–44, simplify using the quotient rule. _____ ³√11/64
- Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. √500x^3/√10x^−1
- In Exercises 1–38, solve each radical equation. (x - 2)¹/² + 8 = 6
- Simplify each exponential expression in Exercises 23–64. (x^11)^5
- Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. -(x^3y^5/z)^0
- In Exercises 33–46, simplify each expression. __ √5²
- In Exercises 25–34, use the zero-exponent rule to simplify each expression. (13y)⁰
- In Exercises 29–44, simplify using the quotient rule. _______ √x²/144y¹²
- In Exercises 33–44, add or subtract terms whenever possible. 8√5+11√5
- In Exercises 1–38, solve each radical equation. ____ _____ √x + 2 + √3x + 7 = 1
- In Exercises 33–38, express the function, f, in simplified form. Assume that x can be any real number. _______...
- Find each root. √12²
- Match each expression in Column I with its equivalent expression in Column II. Choices may be used once, more ...
- Simplify each exponential expression in Exercises 23–64. x^14/x^7
- In Exercises 33–46, simplify each expression. ____ √(−4)²
- In Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. 3⁻²
- In Exercises 21–38, rewrite each expression with rational exponents. ____ (⁶√7xy² ) ⁵
- In Exercises 33–44, add or subtract terms whenever possible. 4√13x−6√13x
- In Exercises 1–38, solve each radical equation. 2(x - 1)¹/³ = (x² + 2x)¹/³
- In Exercises 33–38, express the function, f, in simplified form. Assume that x can be any real number. _______...
- In Exercises 33–46, simplify each expression. _____ √(x−1)²
- In Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. (-5)⁻²
- In Exercises 21–38, rewrite each expression with rational exponents. __ 2x ³√y²
- Find each root. ∛x³
- In Exercises 1–38, solve each radical equation. (x - 2)¹/⁴ = (3x - 8)¹/⁴
- Simplify each exponential expression in Exercises 23–64. x^30/x^−10
- In Exercises 33–38, express the function, f, in simplified form. Assume that x can be any real number. _______...
- Find each root. ⁷√y⁷
- In Exercises 33–44, add or subtract terms whenever possible. √50x−√8x
- In Exercises 33–46, simplify each expression. ____ √36x⁴
- In Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. -5⁻²
- In Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. 49^-½
- Write each expression without negative exponents, and evaluate if possible. Assume all variables represent non...
- In Exercises 39–60, simplify by factoring. Assume that all variables in a radicand represent positive real num...
- Find each root. ⁶√x^6
- Simplify each exponential expression in Exercises 23–64. (−4/x)^3
- In Exercises 33–46, simplify each expression. _____ −√100x⁶
- In Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. x²y⁻³
- In Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. 27^-⅓
- Find each root. √25k⁴m²
- Write each expression without negative exponents, and evaluate if possible. Assume all variables represent non...
- In Exercises 39–60, simplify by factoring. Assume that all variables in a radicand represent positive real num...
- Find each root. ∜81p¹²q⁴
- In Exercises 29–44, simplify using the quotient rule. ______ ⁴√13y⁷/x¹²
- In Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. 16^-¾
- In Exercises 33–44, add or subtract terms whenever possible. 3√8−√32+3√72−√75
- Write each expression without negative exponents, and evaluate if possible. Assume all variables represent non...
- Find each root. ∜(5 + 2m)⁴
- In Exercises 29–44, simplify using the quotient rule. _______ ⁵√64x¹⁴/y¹⁵
- Simplify each exponential expression in Exercises 23–64. (3x^4)(2x^7)
- In Exercises 45–66, divide and, if possible, simplify. ___ √200 √10
- In Exercises 39–64, rationalize each denominator. 1 ----- ³√3
- Use the rules for radicals to perform the indicated operations. Assume all variable expressions represent posi...
- In Exercises 47 - 49, add or subtract terms whenever possible. 7√5 + 13√5
- In Exercises 45–66, divide and, if possible, simplify. __ ³√54 ³√2
- In Exercises 39–64, rationalize each denominator. 10 ----- ³√5
- In Exercises 39–60, simplify by factoring. Assume that all variables in a radicand represent positive real num...
- In Exercises 47 - 49, add or subtract terms whenever possible. 4√72 - 2√48
- In Exercises 47–54, find each cube root. ___ ³√−27
- In Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. x⁻²/y⁻⁵
- In Exercises 50 - 53, rationalize the denominator. 30/√5
- In Exercises 39–64, rationalize each denominator. 3 ³√ ---- 4
- In Exercises 47–54, find each cube root. _____ ³√1/125
- In Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. a⁻⁴b⁷/c⁻³
- In Exercises 45–54, rationalize the denominator. 7/(√5−2)
- In Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. (2xy)^-...
- Use the rules for radicals to perform the indicated operations. Assume all variable expressions represent posi...
- In Exercises 39–64, rationalize each denominator. 7 ----- ³√x
- In Exercises 47–54, find each cube root. ________ ³√−27/1000
- In Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. 5xz^-⅓
- In Exercises 53–58, simplify each expression using the power rule. (x⁶)¹⁰
- Use the rules for radicals to perform the indicated operations. Assume all variable expressions represent posi...
- In Exercises 39–64, rationalize each denominator. 5 ³√ ----- y²
- In Exercises 45–54, rationalize the denominator. 11/(√7−√3)
- Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent nonzero re...
- In Exercises 55–58, find the indicated function values for each function. ___ f(x) = ³√x−1; f(28), f(9), f(0),...
- In Exercises 53–58, simplify each expression using the power rule. (b⁴)⁻³
- Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent nonzero re...
- In Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variable...
- Evaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ³√8
- In Exercises 45–66, divide and, if possible, simplify. ______ √54a⁷b¹¹ √3a⁻⁴b⁻²
- In Exercises 55–58, find the indicated function values for each function. ____ g(x) = −³√8x−8; g(2), g(1), g(0...
- In Exercises 53–58, simplify each expression using the power rule. (7⁻⁴)⁻⁵
- Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent nonzero re...
- In Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variable...
- In Exercises 45–66, divide and, if possible, simplify. ____ √50xy 2√2
- Simplify each exponential expression in Exercises 23–64. 10x^4 y^9/30x^12 y^−3
- Simplify the radical expressions in Exercises 58 - 62. ∛81
- In Exercises 39–64, rationalize each denominator. 3 ³√ ------- xy²
- In Exercises 59–72, simplify each expression using the products-to-powers rule. (4x)³
- In Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variable...
- Evaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ⁴√−16
- In Exercises 45–66, divide and, if possible, simplify. ______ ³√250x⁵y³ ³√2x³
- Simplify each exponential expression in Exercises 23–64. (3x^4/y)^−3
- In Exercises 39–64, rationalize each denominator. 5 ------- ⁴√x
- Simplify the radical expressions in Exercises 58 - 62. 4∛16 + 5∛2
- In Exercises 45–66, divide and, if possible, simplify. ______ ⁵√96x¹²y¹¹ ⁵√3x²y⁻²
- Simplify the radical expressions in Exercises 58 - 62. ∜(32x^5)/∜(16x) (Assume that x > 0.)
- In Exercises 39–64, rationalize each denominator. 10 ---------- ⁵√16x²
- Evaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ⁵√(−3)^5
- Simplify each exponential expression in Exercises 23–64. (3a^−5 b^2/12a^3 b^−4)^0
- In Exercises 45–66, divide and, if possible, simplify. _______ ³√x²+7x+12 ³√x+3
- In Exercises 39–64, rationalize each denominator. 3xy² ----------- ⁵√8xy³
- In Exercises 61–82, multiply and simplify. Assume that all variables in a radicand represent positive real num...
- In Exercises 59–76, find the indicated root, or state that the expression is not a real number. ___ ⁴√−16
- Evaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ⁶√1/64
- In Exercises 65–74, simplify each radical expression and then rationalize the denominator. 25 --------- √5x²y
- In Exercises 59–76, find the indicated root, or state that the expression is not a real number. ___ ⁵√−1
- In Exercises 59–72, simplify each expression using the products-to-powers rule. (-3x⁻²)⁻³
- In Exercises 65–74, simplify each radical expression and then rationalize the denominator. 150a³ - √ --------...
- In Exercises 61–82, multiply and simplify. Assume that all variables in a radicand represent positive real num...
- In Exercises 59–76, find the indicated root, or state that the expression is not a real number. ___ ⁶√−1
- In Exercises 59–72, simplify each expression using the products-to-powers rule. (5x³y⁻⁴)⁻²
- In Exercises 65–74, simplify each radical expression and then rationalize the denominator. 5m⁴n⁶ √ ----------...
- In Exercises 61–82, multiply and simplify. Assume that all variables in a radicand represent positive real num...
- In Exercises 59–76, find the indicated root, or state that the expression is not a real number. ___ −⁴√256
- In Exercises 59–72, simplify each expression using the products-to-powers rule. (-2x⁻⁵y⁴z²)⁻⁴
- Simplify by reducing the index of the radical : [y^3]^(1/6)
- Simplify each radical. Assume all variables represent positive real numbers. √192
- In Exercises 59–76, find the indicated root, or state that the expression is not a real number. __ ⁶√64
- In Exercises 73–84, simplify each expression using the quotients-to-powers rule. (2/x)⁴
- Simplify the radical expressions in Exercises 67–74, if possible. ⁵√64x^6/⁵√2x
- Evaluate each expression. See Example 7. 169^1/2
- In Exercises 65–74, simplify each radical expression and then rationalize the denominator. 15 ------------ ³√...
- Simplify each radical. Assume all variables represent positive real numbers. ∛250
- In Exercises 73–84, simplify each expression using the quotients-to-powers rule. (x³/5)²
- Evaluate each expression. See Example 7. 16^1/4
- In Exercises 75–82, add or subtract terms whenever possible. 4⁵√2+3⁵√2
- Simplify each radical. Assume all variables represent positive real numbers. - ∜243
- In Exercises 75–92, rationalize each denominator. Simplify, if possible. 15 ---------- √6 + 1
- In Exercises 73–84, simplify each expression using the quotients-to-powers rule. (- 3x/y)⁴
- In Exercises 77–90, simplify each expression. Include absolute value bars where necessary. __ ³√x³
- Evaluate each expression. See Example 7. (-64/27)^1/3
- Simplify each radical. Assume all variables represent positive real numbers. -9 ⁵√243
- In Exercises 75–92, rationalize each denominator. Simplify, if possible. 17 ---------- √10 - 2
- Evaluate each expression. See Example 7. (-4)^1/2
- In Exercises 79–112, use rational exponents to simplify each expression. If rational exponents appear after si...
- In Exercises 77–90, simplify each expression. Include absolute value bars where necessary. __ ⁴√y⁴
- In Exercises 75–82, add or subtract terms whenever possible. ³√54xy^3−y³√128x
- In Exercises 75–92, rationalize each denominator. Simplify, if possible. 12 ------------ √7 + √3
- Simplify each radical. Assume all variables represent positive real numbers. ∛(16 (-2)⁴ (2)⁸)
- Match each expression in Column I with its equivalent expression in Column II. See Example 8. a. (4/9)^3/2 b....
- In Exercises 79–112, use rational exponents to simplify each expression. If rational exponents appear after si...
- In Exercises 77–90, simplify each expression. Include absolute value bars where necessary. ____ ³√−8x³
- In Exercises 75–92, rationalize each denominator. Simplify, if possible. √b ---------- √a - √b
- In Exercises 75–82, add or subtract terms whenever possible. √3+³√15
- Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive r...
- In Exercises 79–112, use rational exponents to simplify each expression. If rational exponents appear after si...
- In Exercises 77–90, simplify each expression. Include absolute value bars where necessary. ____ ³√(−5)³
- Simplify each radical. Assume all variables represent positive real numbers. √24m⁶n⁵
- In Exercises 85–116, simplify each exponential expression. x³/x⁹
- Simplify each radical. Assume all variables represent positive real numbers. ∜(x⁴ + y⁴)
- Simplify each radical. Assume all variables represent positive real numbers. ∛(27 + a³)
- In Exercises 85–116, simplify each exponential expression. 20x³/-5x⁴
- Simplify each radical. Assume all variables represent positive real numbers. ⁹√5³
- Simplify each radical. Assume all variables represent positive real numbers. ⁶√11³
- In Exercises 83–90, evaluate each expression without using a calculator. 16^(−6/2)
- Simplify each radical. Assume all variables represent positive real numbers. ⁸√5⁴
- In Exercises 75–92, rationalize each denominator. Simplify, if possible. 2√6 + √5 -------------- 3√6 - √5
- Simplify each radical. Assume all variables represent positive real numbers. ⁶√x¹⁸y²
- Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive r...
- Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive r...
- In Exercises 93–104, rationalize each numerator. Simplify, if possible. 5 √ --- 3
- Simplify each radical. Assume all variables represent positive real numbers. ⁹√∜7³
- In Exercises 91–100, simplify using properties of exponents. (x^2/3)^3
- Perform the indicated operations. Assume all variables represent positive real numbers. 8√(2x) - √(8x) + √(72x...
- In Exercises 85–116, simplify each exponential expression. (2a⁵)(-3a⁻⁷)
- In Exercises 93–104, rationalize each numerator. Simplify, if possible. ³√2x ³√y
- Perform the indicated operations. Assume all variables represent positive real numbers. 3√72m² - 5√32m² - 3√18...
- In Exercises 85–116, simplify each exponential expression. (-¼x⁻⁴y⁵z⁻¹)(-12x⁻³y⁻¹z⁴)
- In Exercises 93–104, rationalize each numerator. Simplify, if possible. √x + 4 √x
- Perform the indicated operations. Assume all variables represent positive real numbers. 2∛3 + 4∛24 - ∛81
- In Exercises 85–116, simplify each exponential expression. 6x²/2x⁻⁸
- In Exercises 93–104, rationalize each numerator. Simplify, if possible. √a - √b √a + √b
- Perform the indicated operations. Assume all variables represent positive real numbers. ∜32 + 3∜2
- In Exercises 85–116, simplify each exponential expression. x⁻⁷/x³
- Evaluate each expression for p=-4, q=8, and r=-10. q+r / q+p
- In Exercises 101–108, simplify by reducing the index of the radical. ⁴√7^2
- Perform the indicated operations. Assume all variables represent positive real numbers. 2∛16 + ∛54
- In Exercises 85–116, simplify each exponential expression. 30x²y⁵/-6x⁸y⁻³
- Evaluate each expression for p=-4, q=8, and r=-10. 3q/r - 5/p
- In Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. |−20| □ |−50...
- Perform the indicated operations. Assume all variables represent positive real numbers. 3x∛xy² - 2∛8x⁴y²
- In Exercises 85–116, simplify each exponential expression. -24a³b⁻⁵c⁵/-3a⁻⁶b⁻⁴c⁻⁷
- Evaluate each expression for p=-4, q=8, and r=-10. 5r / 2p-3r
- In Exercises 105–110, use an associative property to write an algebraic expression equivalent to each expressi...
- In Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. 30/40−3/4 □ ...
- In Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbe...
- Evaluate each expression for p=-4, q=8, and r=-10. q/2-r/3 / 3p/4+q/8
- In Exercises 101–108, simplify by reducing the index of the radical. ⁹√x^6 y^3
- In Exercises 101–108, simplify by reducing the index of the radical. ¹²√x^4y^8
- Evaluate each expression for p=-4, q=8, and r=-10. -(p+2)²-3r / 2-q
- Calculate each value mentally. (0.25^3)(400^3)
- Perform the indicated operations. Assume all variables represent positive real numbers. ∛64xy² + ∛27x⁴y⁵
- Calculate each value mentally. (24^2)(0.5^2)
- In Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbe...
- In Exercises 111–114, simplify each expression. Assume that all variables represent positive numbers. (49x^−2y...
- Perform the indicated operations. Assume all variables represent positive real numbers. ∜81x⁶y³ - ∜16x¹⁰y³
- Calculate each value mentally. 15^4/5^4
- Calculate each value mentally. (0.2^2/3)(40^2/3)
- In Exercises 111–114, simplify each expression. Assume that all variables represent positive numbers. (x^−5/4y...
- Perform the indicated operations. Assume all variables represent positive real numbers. 5√6 + 2√10
- In Exercises 85–116, simplify each exponential expression. (x⁻⁵y⁸/3)⁻⁴
- In Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbe...
- Perform the indicated operations. Assume all variables represent positive real numbers. √6(3 + √7)
- In Exercises 85–116, simplify each exponential expression. (20a⁻³b⁴c⁵/-2a⁻⁵b⁻²c)⁻²
- Calculate each value mentally. (20^2/3)/(5^3/2)
- Perform the indicated operations. Assume all variables represent positive real numbers. 4√3(√7 - 2√11)
- In Exercises 117–124, simplify each exponential expression. 9y⁴/x⁻² + (x⁻¹/y²)⁻²
- Perform the indicated operations. Assume all variables represent positive real numbers. (√2 + 3) (√2 - 3)
- Make Sense? In Exercises 119–122, determine whether each statement makes sense or does not make sense, and exp...
- In Exercises 117–124, simplify each exponential expression. (3x⁴/y⁻⁴)⁻¹(2x/y²)³
- Perform the indicated operations. Assume all variables represent positive real numbers. (∛11 - 1) (∛11² + ∛11 ...
- In Exercises 117–124, simplify each exponential expression. (-4x³y⁻⁵)⁻²(2x⁻⁸y⁻⁵)
- ___ The domain of f(x) = ³√x−4 is [4, ∞).
- In Exercises 117–124, simplify each exponential expression. (2x²y⁴)⁻¹(4xy³)⁻³ / (x²y)⁻⁵(x³y²)⁴
- _ If x=−2, then √x⁶ = x³.
- Perform the indicated operations. Assume all variables represent positive real numbers. (3√2 + √3) (2√3 - √2)
- Perform the indicated operations and/or simplify each expression. Assume all variables represent positive real...
- Between which two consecutive integers is -√26? Do not use a calculator.
- Perform the indicated operations and/or simplify each expression. Assume all variables represent positive real...
- Perform the indicated operations and/or simplify each expression. Assume all variables represent positive real...
- Rationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are ...
- Rationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are ...
- Rationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are ...
- Concept Check: By what number should the numerator and denominator of 1/(∛3 - ∛5) be multiplied in order to ra...