Which is equal to 1/7^10? Choices: (A)(-7)^10 (B)-7^10 (C)7^-10 (D)-1/7^-10

Understand Expression: Understand the given expression 1/7^10. The given expression is a fraction with 1 in the numerator and 7^10 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. Therefore, 1/7^10 can be rewritten using a negative exponent as 7^-10.Compare Equivalent Expressions: Compare the equivalent expression 7^-10 with the given choices. (A) (-7)^10 is not equivalent because it represents a positive value due to the even exponent, and the base is -7 instead of 7. (B) -7^10 is not equivalent because it represents a negative value, and the base is -7 instead of 7. (C) 7^-10 is the correct equivalent expression. (D) -1/7^-10 is not equivalent because it represents a negative value and the negative exponent applies only to 7, not to -1.

Home

Math Problems

Algebra 1

Negative exponents

Full solution

Q. Which is equal to

\frac{1}{7^{10}}

\newline

Choices:

\newline

(A)

(-7)^{10}

\newline

(B)

-7^{10}

\newline

(C)

7^{-10}

\newline

(D)

-\frac{1}{7^{-10}}

Understand Expression: Understand the given expression $\frac{1}{7^{10}}$ . The given expression is a fraction with $1$ in the numerator and $7^{10}$ in the denominator.
Apply Negative Exponent Rule: Identify the equivalent expression using the negative exponent rule. $\newline$ The negative exponent rule states that $a^{-m} = \frac{1}{a^m}$ . Therefore, $\frac{1}{7^{10}}$ can be rewritten using a negative exponent as $7^{-10}$ .
Compare Equivalent Expressions: Compare the equivalent expression $7^{-10}$ with the given choices. $\newline$ (A) $(-7)^{10}$ is not equivalent because it represents a positive value due to the even exponent, and the base is $-7$ instead of $7$ . $\newline$ (B) $-7^{10}$ is not equivalent because it represents a negative value, and the base is $-7$ instead of $7$ . $\newline$ (C) $7^{-10}$ is the correct equivalent expression. $\newline$ (D) $-\frac{1}{7^{-10}}$ is not equivalent because it represents a negative value and the negative exponent applies only to $7$ , not to $(-7)^{10}$ $0$ .