Choose the one alternative that best completes the statement or answers the question.
-If $3 ^ { - x } = \frac { 1 } { 5 }$, what does $9 ^ { x }$ equal?
A) $- 25$
B) 5
C) 25
D) $\frac { 1 } { 25 }$

Question

Quizplus · Accepted Answer

Given $3^{-x} = \frac{1}{5}$, we can rewrite $9^x$ as $(3^2)^x = 3^{2x}$. Since $3^{-x} = \frac{1}{5}$, squaring both sides gives $3^{-2x} = \frac{1}{25}$, which means $3^{2x} = 25$. Thus, $9^x = 25$.

Choose the One Alternative That Best Completes the Statement or Answers