Which is equal to $\frac{1}{54^6}$ ? $\newline$ Choices: $\newline$ (A) $54^{-6}$ $\newline$ (B) $\frac{1}{54^{-6}}$ $\newline$ (C) $-\frac{1}{(-54)^{-6}}$ $\newline$ (D) $\frac{1}{(-54)^{-6}}$

Full solution

Q. Which is equal to

\frac{1}{54^6}

\newline

Choices:

\newline

(A)

54^{-6}

\newline

(B)

\frac{1}{54^{-6}}

\newline

(C)

-\frac{1}{(-54)^{-6}}

\newline

(D)

\frac{1}{(-54)^{-6}}

Understand Expression: Understand the given expression $\frac{1}{54^6}$ . The given expression is a fraction with $1$ in the numerator and $54^6$ in the denominator.
Apply Negative Exponent Rule: Apply the negative exponent rule. $\newline$ The negative exponent rule states that $a^{-m} = \frac{1}{a^m}$ . Therefore, to express $\frac{1}{54^6}$ with a negative exponent, we can write it as $54^{-6}$ .
Match with Choices: Match the expression with the given choices. $\newline$ The expression $54^{-6}$ matches choice (A) $54^{-6}$ .
Verify Other Choices: Verify that the other choices do not match the given expression. $\newline$ (B) $\frac{1}{54^{-6}}$ would be equivalent to $54^6$ , which is not the same as $\frac{1}{54^6}$ . $\newline$ (C) $-\frac{1}{(-54)^{-6}}$ would imply a negative result, which is not the case for $\frac{1}{54^6}$ . $\newline$ (D) $\frac{1}{(-54)^{-6}}$ would also imply a negative result, which is incorrect.