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Which is equal to $\frac{1}{23^8}$ ? $\newline$ Choices: $\newline$ (A) $23^{-8}$ $\newline$ (B) $-23^8$ $\newline$ (C) $(-23)^8$ $\newline$ (D) $-\frac{1}{23^{-8}}$

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Negative exponents

Full solution

Q. Which is equal to

\frac{1}{23^8}

?

\newline

Choices:

\newline

(A)

23^{-8}

\newline

(B)

-23^8

\newline

(C)

(-23)^8

\newline

(D)

-\frac{1}{23^{-8}}

Understand expression: Understand the given expression $\frac{1}{23^8}$ . The expression represents the reciprocal of $23$ raised to the power of $8$ .
Apply negative exponent rule: Apply the negative exponent rule. $\newline$ The negative exponent rule states that $a^{-m} = \frac{1}{a^m}$ . Therefore, to express $\frac{1}{23^8}$ with a negative exponent, we would write it as $23^{-8}$ .
Match with choices: Match the expression with the given choices. $\newline$ The expression $23^{-8}$ matches choice (A) $23^{-8}$ .
Eliminate incorrect choices: Eliminate the incorrect choices. $\newline$ (B) $-23^8$ implies a negative base raised to a positive power, which is not a reciprocal. $\newline$ (C) $(-23)^8$ implies a negative base raised to an even power, which would result in a positive value, not a reciprocal. $\newline$ (D) $-\frac{1}{23^{-8}}$ implies a negative reciprocal of a negative exponent, which is not equivalent to the given expression.

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