Which is equal to 1/83^71? Choices: (A)1/(-83)^71 (B)-(-83)^71 (C)83^-71 (D)83^71

Understand expression: Understand the given expression 1/83^71. The expression represents the reciprocal of 83 raised to the power of 71.Apply negative exponent rule: Identify the equivalent expression for 1/83^71 using the negative exponent rule. Negative exponent rule: a^-m = 1 / a^m Applying this rule, we can rewrite 1/83^71 as 83^-71.Match equivalent expression: Match the equivalent expression 83^-71 with the given choices. (A) 1/(-83)^71 is not equivalent because it includes a negative base. (B) -(-83)^71 is not equivalent because it represents a negative value, not a reciprocal. (C) 83^-71 is the equivalent expression as per the negative exponent rule. (D) 83^71 is not equivalent because it is not the reciprocal of 83^71.

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Math Problems

Algebra 1

Negative exponents

Full solution

Q. Which is equal to

\frac{1}{83^{71}}

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Choices:

\newline

(A)

\frac{1}{(-83)^{71}}

\newline

(B)

-(-83)^{71}

\newline

(C)

83^{-71}

\newline

(D)

83^{71}

Understand expression: Understand the given expression $\frac{1}{83^{71}}$ . The expression represents the reciprocal of $83$ raised to the power of $71$ .
Apply negative exponent rule: Identify the equivalent expression for $1/83^{71}$ using the negative exponent rule. $\newline$ Negative exponent rule: $a^{-m} = 1 / a^{m}$ $\newline$ Applying this rule, we can rewrite $1/83^{71}$ as $83^{-71}$ .
Match equivalent expression: Match the equivalent expression $83^{-71}$ with the given choices. $\newline$ (A) $\frac{1}{(-83)^{71}}$ is not equivalent because it includes a negative base. $\newline$ (B) $-(-83)^{71}$ is not equivalent because it represents a negative value, not a reciprocal. $\newline$ (C) $83^{-71}$ is the equivalent expression as per the negative exponent rule. $\newline$ (D) $83^{71}$ is not equivalent because it is not the reciprocal of $83^{71}$ .