Which is equal to 1/9^25? Choices: (A)-9^25 (B)1/(-9)^-25 (C)-(-9)^25 (D)9^-25

Understand Expression: Understand the given expression 1/9^25. The given expression is a fraction with 1 in the numerator and 9^25 in the denominator.Apply Negative Exponent Rule: Apply the negative exponent rule to rewrite the expression. The negative exponent rule states that a^-m = 1/a^m. Therefore, 1/9^25 can be rewritten as 9^-25.Compare with Choices: Compare the rewritten expression with the given choices. The expression 9^-25 matches choice (D) directly.Verify Other Choices: Verify that the other choices do not match the given expression. (A) -9^25 is not equivalent because it has a negative base and a positive exponent. (B) 1/(-9)^-25 is not equivalent because it has a negative base and a negative exponent. (C) -(-9)^25 is not equivalent because it has a negative base and a positive exponent with an additional negative sign in front.

Home

Math Problems

Algebra 1

Negative exponents

Full solution

Q. Which is equal to

\frac{1}{9^{25}}

\newline

Choices:

\newline

(A)

-9^{25}

\newline

(B)

\frac{1}{(-9)^{-25}}

\newline

(C)

-(-9)^{25}

\newline

(D)

9^{-25}

Understand Expression: Understand the given expression $\frac{1}{9^{25}}$ . The given expression is a fraction with $1$ in the numerator and $9^{25}$ in the denominator.
Apply Negative Exponent Rule: Apply the negative exponent rule to rewrite the expression. $\newline$ The negative exponent rule states that $a^{-m} = \frac{1}{a^m}$ . Therefore, $\frac{1}{9^{25}}$ can be rewritten as $9^{-25}$ .
Compare with Choices: Compare the rewritten expression with the given choices. $\newline$ The expression $9^{-25}$ matches choice (D) directly.
Verify Other Choices: Verify that the other choices do not match the given expression. $\newline$ (A) $-9^{25}$ is not equivalent because it has a negative base and a positive exponent. $\newline$ (B) $\frac{1}{(-9)^{-25}}$ is not equivalent because it has a negative base and a negative exponent. $\newline$ (C) $-(-9)^{25}$ is not equivalent because it has a negative base and a positive exponent with an additional negative sign in front.