\(\begin{array}\ &&\frac{(a+b)^n}{b^n} \\ =&&\big(\frac{a+b}{b}\big)^n \\ =&&\big(\frac{b+a}{b}\big)^n \\ =&&\big(\frac{b}{b}+\frac{a}{b}\big)^n \\ =&&\big(1+\frac{a}{b}\big)^n \\ \end{array}\)