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

Explanation

To prove the rule of exponents \((ab)^n = a^n b^n\) using the principle of mathematical induction for every natural number \(n\), we will follow these steps:

### Step 1: Base Case
We start with the base case where \(n = 1\).

\[ P(1): (ab)^1 = a^1 b^1 \]
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