Question

Find the value of $x$ so that.
$(\frac{2}{5}{)}^3\times (\frac{2}{5}{)}^6=(\frac{2}{5}{)}^{3x}$

Answer 1

$(\frac{2}{3}{)}^3\times (\frac{2}{5}{)}^6=(\frac{2}{5}{)}^{3x}$

$\because$ on L.H.S, bases are same so,

powers are added, i.e

$(\frac{2}{5}{)}^{3+6}=(\frac{2}{5}{)}^{3x}$

$\Rightarrow (\frac{2}{5}{)}^9=(\frac{2}{5}{)}^{3x}$

$\because$ bases are same, so powers

can be equated,

$9=3x$

$x=1$ Ans.