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Which is equal to $\frac{1}{31^{79}}$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{(-31)^{79}}$ $\newline$ (B) $(-31)^{-79}$ $\newline$ (C) $31^{-79}$ $\newline$ (D) $31^{79}$

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Negative exponents

Full solution

Q. Which is equal to

\frac{1}{31^{79}}

?

\newline

Choices:

\newline

(A)

\frac{1}{(-31)^{79}}

\newline

(B)

(-31)^{-79}

\newline

(C)

31^{-79}

\newline

(D)

31^{79}

Understand Expression: Understand the given expression $\frac{1}{31^{79}}$ . The given expression is a fraction with $1$ in the numerator and $31^{79}$ in the denominator.
Apply Negative Exponent Rule: Identify the equivalent expression using the negative exponent rule. $\newline$ The negative exponent rule states that $a^{-m} = \frac{1}{a^m}$ . Therefore, we can rewrite $\frac{1}{31^{79}}$ as $31^{-79}$ .
Match Equivalent Expression: Match the equivalent expression with the given choices. $\newline$ Comparing the expression $31^{-79}$ with the choices given, we find that it matches with choice (C) $31^{-79}$ .

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