MCQ
If $10^{2 y}=25$, then $10^{-y}$ equals:
- A$-\frac{1}{5}$
- B$\frac{1}{50}$
- C$\frac{1}{625}$
- ✓$\frac{1}{5}$
✓
Answer
Correct option: D.
$\frac{1}{5}$
We have to find the value of $10^{-y}$
Given that $10^{2 y}=25$, therefore,
$10^{2 y}=25$
$\left(10^y\right)^2=5^2$
$(10^\text{y})^{2\times\frac{1}{2}}=5^{2\times\frac{1}{2}}$
$\frac{10^{\text{y}}}{1}=\frac{5}{1}$
$\frac{1}{5}=\frac{1}{10^\text{y}}$
$\frac{1}{5}=10^\text{y}$
Hence the correct option is $d.$
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