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Which is equal to $\frac{1}{7^5}$ ? $\newline$ Choices: $\newline$ (A) $-(-7)^5$ $\newline$ (B) $7^5$ $\newline$ (C) $-7^5$ $\newline$ (D) $7^{-5}$

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Understanding negative exponents

Full solution

Q. Which is equal to

\frac{1}{7^5}

?

\newline

Choices:

\newline

(A)

-(-7)^5

\newline

(B)

7^5

\newline

(C)

-7^5

\newline

(D)

7^{-5}

Identify Base and Exponent: Identify the base and the exponent of $7^5$ . In $7^5$ , $7$ is the base raised to the exponent $5$ . Base: $7$ Exponent: $5$
Rewrite as Negative Exponent: Rewrite the expression $\frac{1}{7^5}$ as a whole number with a negative exponent. $\newline$ Move $7^5$ to the numerator and then make the exponent negative to express the reciprocal. $\newline$ $\frac{1}{7^5} = 7^{-5}$
Choose Equivalent Expression: Choose the answer choice that is the equivalent expression for $1 / 7^5$ . $1 / 7^5$ is equivalent to $7^{-5}$ , which matches choice $(D)$ .

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