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Which is equal to $3^{-7}$ ? $\newline$ Choices: $\newline$ (A) $(-3)^{-7}$ $\newline$ (B) $3^{7}$ $\newline$ (C) $-\frac{1}{3^{-7}}$ $\newline$ (D) $\frac{1}{3^{7}}$

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Understanding negative exponents

Full solution

Q. Which is equal to

3^{-7}

?

\newline

Choices:

\newline

(A)

(-3)^{-7}

\newline

(B)

3^{7}

\newline

(C)

-\frac{1}{3^{-7}}

\newline

(D)

\frac{1}{3^{7}}

Understand $3^{-7}$ : Understand the expression $3^{-7}$ . $3^{-7}$ means $1$ divided by $3$ raised to the power of $7$ .
Compare choices: Compare the choices to find an equivalent expression. $\newline$ (A) $(-3)^{-7}$ is not equivalent because it involves $-3$ , not $3$ . $\newline$ (B) $3^7$ is the reciprocal of $3^{-7}$ , so it's not equivalent. $\newline$ (C) $-\frac{1}{3^{-7}}$ is not equivalent because it introduces a negative sign that isn't in the original expression. $\newline$ (D) $\frac{1}{3^7}$ is exactly $3^{-7}$ written in another form.

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