Which is equal to 1/6^94? Choices: (A)6^-94 (B)1/(-6)^-94 (C)6^94 (D)-1/6^-94

Identify base and exponent: Identify the base and the exponent in the given expression 1/6^94. The base is 6 and the exponent is 94. The expression is the reciprocal of 6 raised to the power of 94.Apply negative exponent rule: Apply the negative exponent rule to find an equivalent expression. The negative exponent rule states that a^-m = 1/a^m. Therefore, the expression 1/6^94 can be rewritten using a negative exponent as 6^-94.Compare with choices: Compare the rewritten expression with the given choices. The expression 6^-94 matches choice (A) 6^-94.Verify other choices: Verify that the other choices do not match the given expression. (B) 1/(-6)^-94 is not equivalent because it involves a negative base and a negative exponent. (C) 6^94 is the inverse of the given expression. (D) -1/6^-94 is not equivalent because it introduces a negative sign that is not present in the original expression.

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Math Problems

Algebra 1

Negative exponents

Full solution

Q. Which is equal to

\frac{1}{6^{94}}

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Choices:

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(A)

6^{-94}

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(B)

\frac{1}{(-6)^{-94}}

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(C)

6^{94}

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(D)

-\frac{1}{6^{-94}}

Identify base and exponent: Identify the base and the exponent in the given expression $\frac{1}{6^{94}}$ . The base is $6$ and the exponent is $94$ . The expression is the reciprocal of $6$ raised to the power of $94$ .
Apply negative exponent rule: Apply the negative exponent rule to find an equivalent expression. $\newline$ The negative exponent rule states that $a^{-m} = \frac{1}{a^m}$ . Therefore, the expression $\frac{1}{6^{94}}$ can be rewritten using a negative exponent as $6^{-94}$ .
Compare with choices: Compare the rewritten expression with the given choices. $\newline$ The expression $6^{-94}$ matches choice (A) $6^{-94}$ .
Verify other choices: Verify that the other choices do not match the given expression. $\newline$ (B) $\frac{1}{(-6)^{-94}}$ is not equivalent because it involves a negative base and a negative exponent. $\newline$ (C) $6^{94}$ is the inverse of the given expression. $\newline$ (D) $-\frac{1}{6^{-94}}$ is not equivalent because it introduces a negative sign that is not present in the original expression.