Answer
The property was verified for $n=1$.
The property was verified when $n$ was changed to $n+1$.
Work Step by Step
Prove the property for $n=1$
$(\frac{a}{b})^1=\frac{a}{b}=\frac{a^1}{b^1}$
The property is verified for $n=1$
Assuming that $(\frac{a}{b})^n=\frac{a^n}{b^n}$ for all integers $n\geq1$, we need to prove that $(\frac{a}{b})^{n+1}=\frac{a^{n+1}}{b^{n+1}}$:
$(\frac{a}{b})^{n+1}=(\frac{a}{b})^n(\frac{a}{b})=\frac{a^n}{b^n}\frac{a}{b}=\frac{a^na}{b^nb}=\frac{a^{n+1}}{b^{n+1}}$
