Question

If ${\left(\frac{3}{5}\right)}^3\times {\left(\frac{3}{5}\right)}^3\times {\left[{\left(\frac{1}{2}\right)}^2\right]}^{-2}\times \frac{1}{24}=\frac{m}{5^6}$.Find $m$

Answer 1

${\left(\frac{3}{5}\right)}^3\times {\left(\frac{3}{5}\right)}^3\times {\left[{\left(\frac{1}{2}\right)}^2\right]}^{-2}\times \frac{1}{24}=\frac{m}{5^6}$
$\Rightarrow \frac{3^6}{5^6}\times 2^4\times \frac{1}{2^3\times 3}=\frac{m}{5^6}$
$\Rightarrow \frac{3^5\times 2}{5^6}=\frac{m}{5^6}$
$\Rightarrow m=3^5\times 2$
$\Rightarrow m=243\times 2$
$\Rightarrow m=486$