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Which is equal to $\frac{1}{6^3}$ ? $\newline$ Choices: $\newline$ (A) $-6^3$ $\newline$ (B) $6^{-3}$ $\newline$ (C) $(-6)^{-3}$ $\newline$ (D) $-\frac{1}{(-6)^{-3}}$

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Understanding negative exponents

Full solution

Q. Which is equal to

\frac{1}{6^3}

?

\newline

Choices:

\newline

(A)

-6^3

\newline

(B)

6^{-3}

\newline

(C)

(-6)^{-3}

\newline

(D)

-\frac{1}{(-6)^{-3}}

Identify base and exponent: Identify the base and the exponent of $6^3$ $\newline$ In $6^3$ , $6$ is the base raised to the exponent $3$ . $\newline$ Base: $6$ $\newline$ Exponent: $3$
Rewrite expression with negative exponent: Rewrite the expression $\frac{1}{6^3}$ as a whole number with a negative exponent. $\newline$ Move $6^3$ to the numerator and then make the exponent negative. $\newline$ $\frac{1}{6^3} = 6^{-3}$
Choose equivalent expression: Choose the answer choice that is the equivalent expression for $\frac{1}{6^3}$ . $\frac{1}{6^3}$ is equivalent to $6^{-3}$ , which is choice (B).

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