Which is equal to 1/7^5? Choices: (A)-(-7)^5 (B)7^5 (C)-7^5 (D)7^-5

Identify Base and Exponent: Identify the base and the exponent of 7^5. In 7^5, 7 is the base raised to the exponent 5. Base: 7 Exponent: 5Rewrite as Negative Exponent: Rewrite the expression 1 / 7^5 as a whole number with a negative exponent. Move 7^5 to the numerator and then make the exponent negative to express the reciprocal. 1 / 7^5 = 7^-5Choose Equivalent Expression: Choose the answer choice that is the equivalent expression for 1 / 7^5. 1 / 7^5 is equivalent to 7^-5, which matches choice (D).

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Math Problems

Grade 8

Understanding negative exponents

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Q. Which is equal to

\frac{1}{7^5}

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Choices:

\newline

(A)

-(-7)^5

\newline

(B)

7^5

\newline

(C)

-7^5

\newline

(D)

7^{-5}

Identify Base and Exponent: Identify the base and the exponent of $7^5$ . In $7^5$ , $7$ is the base raised to the exponent $5$ . Base: $7$ Exponent: $5$
Rewrite as Negative Exponent: Rewrite the expression $\frac{1}{7^5}$ as a whole number with a negative exponent. $\newline$ Move $7^5$ to the numerator and then make the exponent negative to express the reciprocal. $\newline$ $\frac{1}{7^5} = 7^{-5}$
Choose Equivalent Expression: Choose the answer choice that is the equivalent expression for $1 / 7^5$ . $1 / 7^5$ is equivalent to $7^{-5}$ , which matches choice $(D)$ .