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Which is equal to $\frac{1}{94^{10}}$ ? $\newline$ Choices: $\newline$ (A) $(-94)^{10}$ $\newline$ (B) $94^{-10}$ $\newline$ (C) $-\frac{1}{94^{-10}}$ $\newline$ (D) $\frac{1}{(-94)^{-10}}$

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Negative exponents

Full solution

Q. Which is equal to

\frac{1}{94^{10}}

?

\newline

Choices:

\newline

(A)

(-94)^{10}

\newline

(B)

94^{-10}

\newline

(C)

-\frac{1}{94^{-10}}

\newline

(D)

\frac{1}{(-94)^{-10}}

Understand Expression: Understand the given expression $\frac{1}{94^{10}}$ . The expression represents the reciprocal of $94$ raised to the $10$ th power.
Apply Negative Exponent Rule: Apply the negative exponent rule. The negative exponent rule states that $a^{-m} = \frac{1}{a^m}$ . Therefore, to express $\frac{1}{94^{10}}$ with a negative exponent, we can write it as $94^{-10}$ .
Compare with Choices: Compare the given choices with the expression $94^{-10}$ .
(A) $(-94)^{10}$ is not equivalent because it does not have a negative exponent and it includes a negative base.
(B) $94^{-10}$ is the expression we derived using the negative exponent rule.
(C) $-\frac{1}{94^{-10}}$ is not equivalent because it introduces an additional negative sign in front of the fraction.
(D) $\frac{1}{(-94)^{-10}}$ is not equivalent because it includes a negative base, which is not present in the original expression.

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