Answer
The property was proved for $n=1$
The property is correct if n is changed by $n+1$
Work Step by Step
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 $n+1$
