Evaluate each expression without using a calculator. 16^-6/2

검증된 단계별 안내

Recognize that the expression is an exponentiation with a negative fractional exponent: $16^{\left(-\frac{6}{2}\right)}$.

Simplify the exponent by dividing the numerator by the denominator: $-\frac{6}{2} = -3$, so the expression becomes $16^{-3}$.

Recall that a negative exponent means taking the reciprocal: $a^{-n} = \frac{1}{a^n}$. So, rewrite $16^{-3}$ as $\frac{1}{16^3}$.

Express 16 as a power of 2, since 16 is \$2^4$, so $16^3$ becomes $(2^4)^3$.

Use the power of a power rule: $(a^m)^n = a^{m \times n}$, so $(2^4)^3 = 2^{4 \times 3} = 2^{12}$. Therefore, the expression is $\frac{1}{2^{12}}$.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

35s

도움이 되었나요?

주요 개념

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

Negative Exponents

A negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent. For example, a^(-n) = 1 / a^n. This concept allows rewriting expressions with negative powers into fractions for easier evaluation.

Exponentiation of Powers

When raising a power to another power, multiply the exponents: (a^m)^n = a^(m*n). This rule simplifies expressions like 16^(-6/2) by combining the exponent terms before evaluating the base.

Simplifying Base Numbers

Expressing the base as a power of a smaller number can simplify calculations. For example, 16 can be written as 2^4, which helps in applying exponent rules more easily and evaluating the expression without a calculator.

Evaluate each expression without using a calculator. 16-6/2