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Ch. R - Review of Basic Concepts
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Lial 13th EditionCh. R - Review of Basic Concepts문제 91
1장, 문제 91

Simplify each expression. Write answers without negative exponents. Assume all variables represent positive real numbers. (31/2)(33/2)

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Identify the expression to simplify: \((3^{1/2})(3^{3/2})\).
Recall the property of exponents that states when multiplying powers with the same base, you add the exponents: \(a^m \times a^n = a^{m+n}\).
Add the exponents: \(\frac{1}{2} + \frac{3}{2} = \frac{4}{2}\).
Simplify the sum of the exponents: \(\frac{4}{2} = 2\).
Rewrite the expression using the simplified exponent: \$3^2$ (which has no negative exponents).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Properties of Exponents

This concept involves rules for manipulating expressions with exponents, such as multiplying powers with the same base by adding their exponents. For example, a^m * a^n = a^(m+n). Understanding these properties is essential for simplifying expressions like (3^(1/2))(3^(3/2)).
추천 영상:
04:06
Rational Exponents

Rational Exponents

Rational exponents represent roots and powers simultaneously, where a^(m/n) means the nth root of a raised to the mth power. For instance, 3^(1/2) is the square root of 3. Recognizing and working with rational exponents helps simplify expressions involving fractional powers.
추천 영상:
04:06
Rational Exponents

Eliminating Negative Exponents

Negative exponents indicate reciprocals, such as a^(-n) = 1/a^n. The problem requires answers without negative exponents, so understanding how to rewrite expressions to avoid negative powers is crucial for presenting the final simplified form correctly.
추천 영상:
6:37
Zero and Negative Rules
관련 실천
교과서 질문

Factor each polynomial. See Example 7. m4−3m2−10m^4-3m^2-10

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교과서 질문

Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, M = {0, 2, 4, 6, 8}, N = {1, 3, 5, 7, 9, 11, 13}, Q = {0, 2, 4, 6, 8, 10, 12}, and R = {0, 1, 2, 3, 4}.Use these sets to find each of the following. Identify any disjoint sets. Q ∩ R′

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교과서 질문

Factor each polynomial. See Example 7. a4−2a2−48a^4-2a^2-48

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교과서 질문

Simplify each radical. Assume all variables represent positive real numbers. x18y26\(\sqrt\)[6]{x^{18}y^2}

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교과서 질문

Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, M = {0, 2, 4, 6, 8}, N = {1, 3, 5, 7, 9, 11, 13}, Q = {0, 2, 4, 6, 8, 10, 12}, and R = {0, 1, 2, 3, 4}.Use these sets to find each of the following. Identify any disjoint sets. M′ ∩ Q

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교과서 질문

Perform each division. See Examples 9 and 10. (3t2+17t+10)/(3t+2)

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