Which is equal to 1/4^34? Choices: (A)-1/(-4)^-34 (B)-1/4^-34 (C)-4^34 (D)4^-34

Understand Expression: Understand the given expression 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. The negative exponent rule states that a^-m = 1/a^m. Therefore, 1/4^34 can be rewritten using a negative exponent as 4^-34.Compare with Choices: Compare the rewritten expression with the given choices. 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. (A) -1/(-4)^-34 introduces a negative sign that is not present in the original expression. (B) -1/4^-34 also introduces a negative sign that is not present in the original expression. (C) -4^34 is not a fraction and does not have a negative exponent.

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Algebra 1

Negative exponents

Full solution

Q. Which is equal to

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

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Choices:

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(A)

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

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(B)

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

\newline

(C)

-4^{34}

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(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.