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5.Find the value of m for which \(5^m ÷ 5^{-3} = 5^5\).

Answer :

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