Question

If $(\frac{1}{5}{)}^{3y}=0.008$ then find the value of $(0.25{)}^y$.

Answer 1

We have, $(\frac{1}{5}{)}^{3y}=0.008$
i.e. $(\frac{1}{5}{)}^{3y}=\frac{8}{1000}$
$\Rightarrow (\frac{1}{5}{)}^{3y}=\frac{1}{125}=(\frac{1}{5}{)}^3$
When bases are equal, the exponent must be equal.
$\therefore 3y=3\Rightarrow y=1$
$\therefore (0.25{)}^y=(0.25{)}^1=0.25$