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Which is equal to $\frac{1}{7^4}$ ? $\newline$ Choices: $\newline$ (A) $-7^4$ $\newline$ (B) $7^{-4}$ $\newline$ (C) $-\frac{1}{7^{-4}}$ $\newline$ (D) $-(-7)^4$

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Understanding negative exponents

Full solution

Q. Which is equal to

\frac{1}{7^4}

?

\newline

Choices:

\newline

(A)

-7^4

\newline

(B)

7^{-4}

\newline

(C)

-\frac{1}{7^{-4}}

\newline

(D)

-(-7)^4

Identify base and exponent: Identify the base and the exponent of $7^4$ $\newline$ In $7^4$ , $7$ is the base raised to the exponent $4$ . $\newline$ Base: $7$ $\newline$ Exponent: $4$
Rewrite expression with negative exponent: Rewrite the expression $\frac{1}{7^4}$ as a whole number with a negative exponent. $\newline$ Move $7^4$ to the numerator and then make the exponent negative. $\newline$ $\frac{1}{7^4} = 7^{-4}$
Choose equivalent expression: Choose the answer choice that is the equivalent expression for $1 / 7^4$ . $\newline$ $1 / 7^4$ is equivalent to $7^{-4}$ , which is choice (B).

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