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Which is equal to $3^{-49}$ ? $\newline$ Choices: $\newline$ (A) $(-3)^{-49}$ $\newline$ (B) $\frac{1}{3^{49}}$ $\newline$ (C) $-(-3)^{49}$ $\newline$ (D) $\frac{1}{(-3)^{-49}}$

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Negative exponents

Full solution

Q. Which is equal to

3^{-49}

?

\newline

Choices:

\newline

(A)

(-3)^{-49}

\newline

(B)

\frac{1}{3^{49}}

\newline

(C)

-(-3)^{49}

\newline

(D)

\frac{1}{(-3)^{-49}}

Understand expression: Understand the expression $3^{-49}$ . Identify the base and the exponent. In $3^{-49}$ , $3$ is the base raised to the exponent $-49$ . Base: $3$ Exponent: $-49$
Apply negative exponent rule: Apply the negative exponent rule to $3^{-49}$ . $\newline$ Negative exponent rule: $\newline$ $a^{-m} = \frac{1}{a^{m}}$ $\newline$ So, $3^{-49} = \frac{1}{3^{49}}$
Match with given choices: Match the expression $\frac{1}{3^{49}}$ with the given choices. $\newline$ (A) $(-3)^{-49}$ is not correct because the base is $-3$ , not $3$ . $\newline$ (B) $\frac{1}{3^{49}}$ is the correct expression, as it matches the result from Step $2$ . $\newline$ (C) $-(-3)^{49}$ is not correct because it represents a negative value, not a reciprocal. $\newline$ (D) $\frac{1}{(-3)^{-49}}$ is not correct because the base is $-3$ and the exponent is $-49$ , which would result in a double negative exponent, not matching our result.

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