Simplify each expression. (93)(95)

Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063당신이 사용하는 게 아니라요?교과서 변경

모든 교과서

Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 15

1장, 문제 15

Simplify each expression. (9³)(9⁵)

검증된 단계별 안내

Identify the base and the exponents in the expression $(9^{3})(9^{5})$. Here, the base is 9 for both terms.

Recall the exponent rule for multiplication with the same base: $a^{m} \times a^{n} = a^{m+n}$.

Apply the rule by adding the exponents: $9^{3} \times 9^{5} = 9^{3+5}$.

Simplify the exponent sum: $9^{3+5} = 9^{8}$.

Write the simplified expression as \$9^{8}$, which is the product of the original terms expressed with a single exponent.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

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

Laws of Exponents

The laws of exponents provide rules for simplifying expressions involving powers. One key rule states that when multiplying two expressions with the same base, you add their exponents. For example, a^m * a^n = a^(m+n). This rule is essential for simplifying (9^3)(9^5).

Base and Exponent

In an expression like 9^3, 9 is the base and 3 is the exponent, indicating how many times the base is multiplied by itself. Understanding the roles of base and exponent helps in applying exponent rules correctly during simplification.

Simplification of Exponential Expressions

Simplification involves rewriting expressions in a simpler or more compact form without changing their value. For exponential expressions, this often means combining like bases using exponent rules to reduce the expression to a single power.