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

We have given: $$5^m ÷ 5^{-3} = 5^5$$.

$$\Rightarrow 5^{m-(-3)} = 5^5\quad$$ [∵$$a^m ÷ a^n = a^{m-n}$$]

$$\Rightarrow 5^{m+3} = 5^5$$

Now, Comparing the powers of equal bases, we have m + 3 = 5

$$\Rightarrow m = 5 – 3 = 2$$, i.e., m = 2