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Which is equal to $5^{-8}$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{5^8}$ $\newline$ (B) $(-5)^8$ $\newline$ (C) $-\frac{1}{5^{-8}}$ $\newline$ (D) $-5^8$

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Understanding negative exponents

Full solution

Q. Which is equal to

5^{-8}

?

\newline

Choices:

\newline

(A)

\frac{1}{5^8}

\newline

(B)

(-5)^8

\newline

(C)

-\frac{1}{5^{-8}}

\newline

(D)

-5^8

Understand expression: Step $1$ : Understand the expression $5^{-8}$ . $5^{-8}$ means $1$ divided by $5$ raised to the power of $8$ . Calculation: $5^{-8} = 1 / 5^8$
Match with choices: Step $2$ : Match the expression with the given choices. $\newline$ We need to find which choice equals $1 / 5^8$ . $\newline$ (A) $1/5^8$ - This matches our calculation. $\newline$ (B) $(-5)^8$ - This is positive because any even power of a negative number is positive. $\newline$ (C) $-1/5^{-8}$ - This simplifies to $-5^8$ , which is negative. $\newline$ (D) $-5^8$ - This is just a negative number, not a reciprocal.

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