Question

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

Answer 1

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