Question

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

Answer 1

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$