Which is equal to 1/83^81? Choices: (A)(-83)^81 (B)83^-81 (C)-83^81 (D)-1/83^-81

Understand Expression: Understand the given expression 1/83^81. The expression is a fraction with 1 in the numerator and 83^81 in the denominator.Apply Negative Exponent Rule: Identify the equivalent expression using the negative exponent rule. The negative exponent rule states that a^-m = 1 / a^m. Applying this rule in reverse, we can write 1 / a^m as a^-m. Therefore, 1/83^81 can be written as 83^-81.Match Equivalent Expression: Match the equivalent expression with the given choices. Comparing the expression 83^-81 with the choices given: (A) (-83)^81 is not equivalent because it represents a negative base raised to an odd power, which would be negative. (B) 83^-81 is the exact match to our equivalent expression. (C) -83^81 is not equivalent because it represents a negative base raised to an odd power, which would be negative. (D) -1/83^-81 is not equivalent because it introduces an additional negative sign in the numerator.

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Math Problems

Algebra 1

Negative exponents

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Q. Which is equal to

\frac{1}{83^{81}}

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Choices:

\newline

(A)

(-83)^{81}

\newline

(B)

83^{-81}

\newline

(C)

-83^{81}

\newline

(D)

-\frac{1}{83^{-81}}

Understand Expression: Understand the given expression $1/83^{81}$ . The expression is a fraction with $1$ in the numerator and $83^{81}$ in the denominator.
Apply Negative Exponent Rule: Identify the equivalent expression using the negative exponent rule. $\newline$ The negative exponent rule states that $a^{-m} = \frac{1}{a^m}$ . Applying this rule in reverse, we can write $\frac{1}{a^m}$ as $a^{-m}$ . Therefore, $\frac{1}{83^{81}}$ can be written as $83^{-81}$ .
Match Equivalent Expression: Match the equivalent expression with the given choices. $\newline$ Comparing the expression $83^{-81}$ with the choices given: $\newline$ (A) $(-83)^{81}$ is not equivalent because it represents a negative base raised to an odd power, which would be negative. $\newline$ (B) $83^{-81}$ is the exact match to our equivalent expression. $\newline$ (C) $-83^{81}$ is not equivalent because it represents a negative base raised to an odd power, which would be negative. $\newline$ (D) $-\frac{1}{83^{-81}}$ is not equivalent because it introduces an additional negative sign in the numerator.