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Which is equal to $\frac{1}{4^5}$ ? $\newline$ Choices: $\newline$ (A) $-\frac{1}{(-4)^{-5}}$ $\newline$ (B) $\frac{1}{(-4)^5}$ $\newline$ (C) $\frac{1}{4^{-5}}$ $\newline$ (D) $4^{-5}$

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Understanding negative exponents

Full solution

Q. Which is equal to

\frac{1}{4^5}

?

\newline

Choices:

\newline

(A)

-\frac{1}{(-4)^{-5}}

\newline

(B)

\frac{1}{(-4)^5}

\newline

(C)

\frac{1}{4^{-5}}

\newline

(D)

4^{-5}

Understand expression: Step $1$ : Understand the expression $\frac{1}{4^5}$ . $\frac{1}{4^5}$ means $1$ divided by $4$ raised to the power of $5$ .
Rewrite using negative exponents: Step $2$ : Rewrite the expression using negative exponents. $\newline$ $\frac{1}{4^5}$ can be rewritten as $4^{-5}$ because moving the base $4$ to the numerator changes the sign of the exponent.
Match with choices: Step $3$ : Match the rewritten expression with the given choices. $\newline$ The expression $4^{-5}$ matches with choice (D).

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