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Which is equal to $\frac{1}{3^4}$ ? $\newline$ Choices: $\newline$ (A) $3^4$ $\newline$ (B) $-\frac{1}{3^{-4}}$ $\newline$ (C) $3^{-4}$ $\newline$ (D) $-(-3)^4$

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Understanding negative exponents

Full solution

Q. Which is equal to

\frac{1}{3^4}

?

\newline

Choices:

\newline

(A)

3^4

\newline

(B)

-\frac{1}{3^{-4}}

\newline

(C)

3^{-4}

\newline

(D)

-(-3)^4

Understand Expression: Understand the expression $\frac{1}{3^4}$ . $\newline$ Rewrite $\frac{1}{3^4}$ using negative exponents. $\newline$ $\frac{1}{3^4} = 3^{-4}$
Rewrite Using Negative Exponents: Match the expression $3^{-4}$ with the given choices. $\newline$ (A) $3^4$ - This is the positive exponent form, not equivalent. $\newline$ (B) $-\frac{1}{3^{-4}}$ - This introduces a negative sign, not equivalent. $\newline$ (C) $3^{-4}$ - This matches exactly with our rewritten expression. $\newline$ (D) $-(-3)^4$ - This changes the base and introduces a negative sign, not equivalent.

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