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Which is equal to $\frac{1}{8^2}$ ? $\newline$ Choices: $\newline$ (A) $-\frac{1}{8^{-2}}$ $\newline$ (B) $8^{-2}$ $\newline$ (C) $\frac{1}{8^{-2}}$ $\newline$ (D) $-\frac{1}{(-8)^{-2}}$

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Understanding negative exponents

Full solution

Q. Which is equal to

\frac{1}{8^2}

?

\newline

Choices:

\newline

(A)

-\frac{1}{8^{-2}}

\newline

(B)

8^{-2}

\newline

(C)

\frac{1}{8^{-2}}

\newline

(D)

-\frac{1}{(-8)^{-2}}

Identify base and exponent: Step $1$ : Identify the base and the exponent in $8^2$ . In $8^2$ , $8$ is the base raised to the exponent $2$ . Base: $8$ Exponent: $2$
Rewrite using negative exponent: Step $2$ : Rewrite the expression $\frac{1}{8^2}$ using a negative exponent. $\newline$ Move $8^2$ to the numerator and make the exponent negative. $\newline$ $\frac{1}{8^2} = 8^{-2}$
Match with choices: Step $3$ : Match the rewritten expression with the given choices. $\newline$ $\frac{1}{8^2} = 8^{-2}$ $\newline$ The correct choice that matches this expression is (B) $8^{-2}$ .

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