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Which is equal to $\frac{1}{4^{34}}$ ? $\newline$ Choices: $\newline$ (A) $-\frac{1}{(-4)^{-34}}$ $\newline$ (B) $-\frac{1}{4^{-34}}$ $\newline$ (C) $-4^{34}$ $\newline$ (D) $4^{-34}$

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Negative exponents

Full solution

Q. Which is equal to

\frac{1}{4^{34}}

?

\newline

Choices:

\newline

(A)

-\frac{1}{(-4)^{-34}}

\newline

(B)

-\frac{1}{4^{-34}}

\newline

(C)

-4^{34}

\newline

(D)

4^{-34}

Understand Expression: Understand the given expression $\frac{1}{4^{34}}$ . The given expression is a fraction with $1$ in the numerator and $4^{34}$ in the denominator.
Apply Negative Exponent Rule: Apply the negative exponent rule to the denominator. $\newline$ The negative exponent rule states that $a^{-m} = \frac{1}{a^m}$ . Therefore, $\frac{1}{4^{34}}$ can be rewritten using a negative exponent as $4^{-34}$ .
Compare with Choices: Compare the rewritten expression with the given choices. $\newline$ The expression $4^{-34}$ matches choice (D), which is $4^{-34}$ .
Verify Other Choices: Verify that the other choices do not match the given expression. $\newline$ (A) $-1/(-4)^{-34}$ introduces a negative sign that is not present in the original expression. $\newline$ (B) $-1/4^{-34}$ also introduces a negative sign that is not present in the original expression. $\newline$ (C) $-4^{34}$ is not a fraction and does not have a negative exponent.

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