Algebra and Trigonometry 10th Edition

The property was proved for $n=1$ The property is correct if n is changed by $n+1$
Let's prove the property for $n=1$: $(ab)^n=(ab)^1=ab=a^1b^1$ It is correct! Suppose that the propety is correct, that is: $(ab)^n=a^nb^n$ for all integers $n\geq1$ Now, let's prove the property for $n+1$: $(ab)^{n+1}=(ab)^n(ab)^1=a^nb^nab=(a^na)(b^nb)=a^{n+1}b^{n+1}$ That is the given property if $n$ is changed by $n+1$
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