Question

Find the value of $m$ for which
$5^m÷5^{-3}=5^5$

Answer 1

Given $5^m÷5^{-3}=5^5\Rightarrow 5^{m-(-3)}=5^5[\because a^m÷a^n=a^{m-n}]$
$\Rightarrow 5^{m+3}=5^5$
On both the sides powers have the same base, so their exponents must be equal.
$\Rightarrow m+3=5$
$\Rightarrow m=5-3$
$\therefore m=2$