Prove the rule of exponents `(a b)^n=a^n b^n`by using principle of mathematical induction for every natural number.

Explanation

Let P(n) be the given statement i.e., P(n):`(ab)^n=a^nb^n`


We note that P(n) is true for n=1 since `(ab)^1=a^1b^1`.


Let P(k) be true, i.e., `(ab)^k=a^kb^k`----------(1)


We shall now prove that `P(k+1)` is true whenever `P(k)` is true.


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