Question

The value of $\frac{(16{)}^5}{(12{)}^5}\times \frac{(24{)}^5}{(32{)}^5}$ is

Answer 1

$\frac{(16{)}^5}{(12{)}^5}\times \frac{(24{)}^5}{(32{)}^5}=\frac{(16{)}^5}{(32{)}^5}\times \frac{(24{)}^5}{(12{)}^5}$
$={\left(\frac{16}{32}\right)}^5\times {\left(\frac{24}{12}\right)}^5$
$={\left(\frac{1}{2}\right)}^5\times (2{)}^5$
$=\frac{1}{2^5}\times 2^5$
$=1$