Which is equal to 1/54^5? Choices: (A)-54^5 (B)(-54)^5 (C)54^-5 (D)-1/54^-5

Understand given expression: Understand the given expression 1/54^5. The given expression is a fraction with 1 in the numerator and 54^5 in the denominator. We need to find an equivalent expression among the choices given.Analyze choices: Analyze the choices to find an equivalent expression. (A) -54^5 is not equivalent because it represents a negative value, while 1/54^5 is positive. (B) (-54)^5 is not equivalent because it represents a negative value due to the odd exponent, while 1/54^5 is positive. (C) 54^-5 uses the negative exponent rule, which states that a^-m = 1/a^m. This looks like the correct equivalent expression for 1/54^5. (D) -1/54^-5 is not equivalent because it represents a negative value, while 1/54^5 is positive.Confirm correct choice: Confirm the correct choice by applying the negative exponent rule. According to the negative exponent rule, 54^-5 is equal to 1/54^5. Therefore, the correct choice is (C) 54^-5.

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Math Problems

Algebra 1

Negative exponents

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Q. Which is equal to

\frac{1}{54^5}

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Choices:

\newline

(A)

-54^5

\newline

(B)

(-54)^5

\newline

(C)

54^{-5}

\newline

(D)

-\frac{1}{54^{-5}}

Understand given expression: Understand the given expression $\frac{1}{54^5}$ . The given expression is a fraction with $1$ in the numerator and $54^5$ in the denominator. We need to find an equivalent expression among the choices given.
Analyze choices: Analyze the choices to find an equivalent expression. $\newline$ (A) $-54^5$ is not equivalent because it represents a negative value, while $\frac{1}{54^5}$ is positive. $\newline$ (B) $(-54)^5$ is not equivalent because it represents a negative value due to the odd exponent, while $\frac{1}{54^5}$ is positive. $\newline$ (C) $54^{-5}$ uses the negative exponent rule, which states that $a^{-m} = \frac{1}{a^m}$ . This looks like the correct equivalent expression for $\frac{1}{54^5}$ . $\newline$ (D) $-\frac{1}{54^{-5}}$ is not equivalent because it represents a negative value, while $\frac{1}{54^5}$ is positive.
Confirm correct choice: Confirm the correct choice by applying the negative exponent rule. $\newline$ According to the negative exponent rule, $54^{-5}$ is equal to $1/54^{5}$ . Therefore, the correct choice is (C) $54^{-5}$ .