Which is equal to 1/6^92? Choices: (A)-1/6^-92 (B)6^92 (C)6^-92 (D)-1/(-6)^-92

Understand Expression: Understand the given expression 1/6^92. The expression represents the reciprocal of 6 raised to the power of 92.Apply Negative Exponent Rule: Apply the negative exponent rule. The negative exponent rule states that a^-m = 1/a^m. Therefore, we can rewrite 1/6^92 as 6^-92.Compare with Choices: Compare the given choices with the transformed expression. We have transformed the original expression to 6^-92. Now we need to find the choice that matches this expression. (A) -1/6^-92 does not match because of the negative sign in front. (B) 6^92 does not match because it is the reciprocal of the original expression. (C) 6^-92 matches exactly with our transformed expression. (D) -1/(-6)^-92 does not match because of the negative signs.

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Math Problems

Algebra 1

Negative exponents

Full solution

Q. Which is equal to

\frac{1}{6^{92}}

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Choices:

\newline

(A)

-\frac{1}{6^{-92}}

\newline

(B)

6^{92}

\newline

(C)

6^{-92}

\newline

(D)

-\frac{1}{(-6)^{-92}}

Understand Expression: Understand the given expression $\frac{1}{6^{92}}$ . The expression represents the reciprocal of $6$ raised to the power of $92$ .
Apply Negative Exponent Rule: Apply the negative exponent rule. $\newline$ The negative exponent rule states that $a^{-m} = \frac{1}{a^m}$ . Therefore, we can rewrite $\frac{1}{6^{92}}$ as $6^{-92}$ .
Compare with Choices: Compare the given choices with the transformed expression. $\newline$ We have transformed the original expression to $6^{-92}$ . Now we need to find the choice that matches this expression. $\newline$ (A) $-\frac{1}{6^{-92}}$ does not match because of the negative sign in front. $\newline$ (B) $6^{92}$ does not match because it is the reciprocal of the original expression. $\newline$ (C) $6^{-92}$ matches exactly with our transformed expression. $\newline$ (D) $-\frac{1}{(-6)^{-92}}$ does not match because of the negative signs.