1. Fundamental Concepts of Algebra

Simplify Exponential Expressions

Exponents and Scientific Notation

Exponents and integers

Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers. √27

In Exercises 29–34, find the union of the sets. {e,m,p,t,y} ∪ ∅

In Exercises 83–90, evaluate each expression without using a calculator. 27^(1/3)

Understanding Exponents and Their Operations

Use the quotient rule to simplify the expressions in Exercises 45-46. √(121/4)

Simplifying Radical Expressions Involving Variables - Example 1

In Exercises 65–76, write each number in decimal notation without the use of exponents. −3.14×10^−3

In Exercises 61–66, evaluate each algebraic expression for x=2 and y=-5. |x|+|y|

In Exercises 77–86, write each number in scientific notation. 0.0083

In Exercises 21–28, find the intersection of the sets. {s,e,t}∩{t,e,s}

In Exercises 65–76, write each number in decimal notation without the use of exponents. −8.17×10^6

Simplifying Expressions with Negative Exponents - Ex 1

Simplify an Algebraic Expression by Combining Like Terms

In Exercises 77–86, write each number in scientific notation. −3829

In Exercises 87–106, perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (6.1×10^−8)(2×10^−4)

Exponent Rules: The Power to Power Rule!

Simplify each exponential expression: (-5x^3y^2)(-2x^(-11)y^(-2))

Applying the Rules of Exponents - Basic Examples #1

In Exercises 35–38, list all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. {-9, -4/5, 0, 0.25, √3, 9.2, √100}

In Exercises 51–60, rewrite each expression without absolute value bars. ||-3|-|-7||

State the name of the property illustrated: 3+17 = 17+3

Power of a Quotient Property

Power of a Product Property

Simplifying Expressions with Negative Exponents - Ex 2

Perform the indicated operation and write the answer in decimal notation. (3*10^3)(1.3*10^2)

In Exercises 51–60, rewrite each expression without absolute value bars. |12 - π|

Simplify expressions with 0 and negative exponents

Simplifying expressions using the Laws of Exponents

In Exercises 67–74, express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. 2 and 17

Simplify each exponential expression in Exercises 23–64. (−3x^2 y^5)^2

Simplify each exponential expression: (-2x^4y^3)^3

Negative Exponents

Write each number in decimal notation: 7.45*10^(-5)

Multiply numbers expressed in scientific notation

In Exercises 51–60, rewrite each expression without absolute value bars. |7 - π|

Power of a Quotient Rule

Applying the Rules of Exponents - Basic Examples #3

In Exercises 75–84, state the name of the property illustrated. 6+(2+7)=(6+2)+7

Let A = {a, b, c}, B = {a, c, d, e}, and C = {a, d, f, g}. Find the indicated set A ∩ B.

Simplify each exponential expression in Exercises 23–64. (−5x^4 y)(−6x^7 y^11)

GED Sample Test with Solutions , Question #42

Divide exponential expressions (part 2)

In Exercises 35–38, list all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. {-11, -5/6, 0, 0.75, √5, π, √64}

In Exercises 87–106, perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (2.4×10^−2)/(4.8×10^-6)

In Exercises 77–86, write each number in scientific notation. 579,000,000,000,000,000

Simplify expressions with 0 and negative exponents 

Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers. √125x^2

Simplify exponential multiplication expressions

Divide exponential expressions (part 1)

Simplifying Expressions with Negative Exponents - Ex 3

In Exercises 75–84, state the name of the property illustrated. 7⋅(11⋅8)=(11⋅8)⋅7

Simplify using properties of exponents. [5x^(2/3)][4x^(1/4)]

Evaluate each exponential expression: (3^3)/(3^6)

In Exercises 75–84, state the name of the property illustrated. 1/(x+3) (x+3)=1, x≠−3

Write each number in scientific notation. 3,590,000

Intro to Evaluating Exponents - A few True/False Questions - Ex1

Power of a Product Rule

In Exercises 61–66, evaluate each algebraic expression for x=2 and y=-5. |x+y|

Divide numbers in scientific notation

Raise an exponential expression to a power

Evaluate each exponential expression: (-3)^3 (-2)^2

Determine whether each statement in Exercises 43–50 is true or false. -π ≥ - π

Evaluate each exponential expression: 2^(-4) + 4^(-1)

State the name of the property illustrated: (6 • 3) • 9 = 6 • (3 • 9)

Use the product rule to simplify the expressions in Exercises 41 - 44. In exercises 43 - 44, assume that variables represent nonnegative real numbers. √300

Identifying Like Terms

In Exercises 91–100, simplify using properties of exponents. (20x^1/2)/(5x^1/4)

The formula C=5/9(F-32) expresses the relationship between Fahrenheit temperature, F, and Celsius temperature, C. In Exercises 17–18, use the formula to convert the given Fahrenheit temperature to its equivalent temperature on the Celsius scale. 50 °F

Zero Exponent Rule

Evaluate each exponential expression: 5^(-3) • 5

Let A = {a, b, c}, B = {a, c, d, e}, and C = {a, d, f, g}. Find the indicated set A ∪ B.

In Exercises 21–28, find the intersection of the sets. {a,b,c,d}∩∅

Multiply two or more exponential expressions

In Exercises 87–106, perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (8.4×10^8)/(4×10^5)

Simplifying Expressions with Negative Exponents 

State the name of the property illustrated: (3 • 7) + (4 • 7) = (4 • 7) + (3 •7)

Numbers with an Exponent of Zero

In Exercises 67–74, express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. -26 and -3

Convert from standard to scientific notation

In Exercises 67–74, express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. −2 and 5

In Exercises 83–90, evaluate each expression without using a calculator. 36^(1/2)

Applying the Rules of Exponents - Basic Examples #2

Exponent Rules: Product to a Power Explained!

Converting Between Scientific Notation and Decimal Notation

Exercises 159–161 will help you prepare for the material covered in the next section. If 6.2 is multiplied by 10^3, what does this multiplication do to the decimal point in 6.2?

In Exercises 87–106, perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (4.3×10^8)(6.2×10^4)

Simplify expressions with negative exponents

In Exercises 51–60, rewrite each expression without absolute value bars. -3/|-3|

In Exercises 87–106, perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (66,000×0.001)/(0.003×0.002)

In Exercises 21–28, find the intersection of the sets. {1,2,3,4}∩{2,4,5}

Determine whether each statement in Exercises 43–50 is true or false. -13 ≤ -2

In Exercises 29–34, find the union of the sets. {1,3,5,7}∪{2,4,6,8,10}

In Exercises 51–60, rewrite each expression without absolute value bars. |300|

In Exercises 87–106, perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (1.2×10^4)/(2×10^−2)

Zero exponent property

Algebra - Simplify an expression with exponents

In Exercises 65–76, write each number in decimal notation without the use of exponents. −7.00001×10^10

A football was kicked vertically upward from a height of 4 feet with an initial speed of 60 feet per second. The formula h=4+60t-16t^2 describes the ball’s height above the ground, h, in feet, t seconds after it was kicked. Use this formula to solve Exercises 19–20. What was the ball’s height 2 seconds after it was kicked?

In Exercises 75–84, state the name of the property illustrated. 6+(−4)=(−4)+6

In Exercises 65–76, write each number in decimal notation without the use of exponents. 9.2×10^2

In Exercises 87–106, perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. 282,000,000,000/0.00141

In Exercises 77–86, write each number in scientific notation. −0.00000000405

Determine whether each statement in Exercises 43–50 is true or false. 0 ≥ -6

In Exercises 77–86, write each number in scientific notation. 64,000

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