Question

If ${10}^{2y}=25$ then ${10}^{-y}$ equals to

• A. $-\frac{1}{5}$
• B. $\frac{1}{50}$
• C. $\frac{1}{625}$
• D. $\frac{1}{5}$

Answer 1

The correct option is D

$\frac{1}{5}$

Explanation for the correct option:

It is given that ${10}^{2y}=25$. It can be simplified as follows:

$\begin{array}{ccc}& {10}^{2y}=25& \\ \Rightarrow & {\left({10}^y\right)}^2=5^2& \left[\because a^{m\times n}={\left(a^m\right)}^n\right]\\ \Rightarrow & {10}^y=5& \\ \Rightarrow & {10}^{-y}=5^{-1}& \\ \Rightarrow & {10}^{-y}=\frac{1}{5}& \end{array}$

Therefore, option D is correct.