Question

The value of $a$ if $(-5{)}^{a+4}\times (-5{)}^8=(-5{)}^{16}$ is___

Answer 1

Answer: 4

We have, $(-5{)}^{a+4}\times (-5{)}^8=(-5{)}^{16}$
$(-5{)}^{a+4+8}=(-5{)}^{16}\left\{\because a^m\times a^n=a^{m+n}\right\}$
$\Rightarrow (-5{)}^{a+12}=(-5{)}^{16}$
On the both sides powers have the same base
$\Rightarrow a+12=16$
$\Rightarrow a=16-12=4$
$\Rightarrow a=4$