Which is equal to $\frac{1}{83^{81}}$ ? $\newline$ Choices: $\newline$ (A) $(-83)^{81}$ $\newline$ (B) $83^{-81}$ $\newline$ (C) $-83^{81}$ $\newline$ (D) $-\frac{1}{83^{-81}}$

Full solution

Q. Which is equal to

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

\newline

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.