Exponents Of Real Numbers — MATHS STD 9 — Question
Rajasthan BoardEnglish MediumSTD 9MATHSExponents Of Real Numbers1 Mark
MCQ
If $10^{2y}{ }= 25,$ 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 $10^{2y}{ }= 25,$
$\therefore 10{2y}^{ }= 25$
$(10^y)^2 = 5^2$
$(10^\text{y})^{2\times\frac{1}{2}}=5^{2\times\frac{1}{2}}$
$\frac{10^{\text{y}}}{1}=\frac{5}{1}$
$\frac{1}{5}=\frac{1}{10^\text{y}}$
$\frac{1}{5}=10^\text{y}$
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