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Which is equal to $9^{-4}$ ? $\newline$ Choices: $\newline$ (A) $-9^4$ $\newline$ (B) $\frac{1}{9^4}$ $\newline$ (C) $\frac{-1}{(-9)^{-4}}$ $\newline$ (D) $\frac{1}{(-9)^{-4}}$

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Understanding negative exponents

Full solution

Q. Which is equal to

9^{-4}

?

\newline

Choices:

\newline

(A)

-9^4

\newline

(B)

\frac{1}{9^4}

\newline

(C)

\frac{-1}{(-9)^{-4}}

\newline

(D)

\frac{1}{(-9)^{-4}}

Understand $9^{-4}$ : Understand the expression $9^{-4}$ . $9^{-4}$ means $1$ divided by $9$ raised to the power of $4$ . Calculation: $9^{-4} = 1 / 9^4$
Compare choices: Compare the choices given. $\newline$ (A) $-9^4$ is not correct because it represents $-6561$ , not a fraction. $\newline$ (B) $\frac{1}{9^4}$ is exactly what $9^{-4}$ simplifies to. $\newline$ (C) $-\frac{1}{(-9)^{-4}}$ simplifies to $-1$ times $-\frac{1}{6561}$ , which is $\frac{1}{6561}$ , not $1/6561$ . $\newline$ (D) $\frac{1}{(-9)^{-4}}$ simplifies to $-6561$ $0$ divided by $-\frac{1}{6561}$ , which is $-6561$ , not a fraction.

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