How do you simplify 4^n/(3^(n-1))?

Multiply the expression by $1$ or $\frac{3}{3}$:
$\frac{3}{3} \cdot {4}^{n} / {3}^{n - 1} = \frac{3 \cdot {4}^{n}}{3 \cdot {3}^{n - 1}} = \frac{3 \cdot {4}^{n}}{{3}^{1} \cdot {3}^{n - 1}} =$
$\frac{3 \cdot {4}^{n}}{{3}^{1 + n - 1}} = \frac{3 \cdot {4}^{n}}{3} ^ n = 3 \cdot {4}^{n} / {3}^{n} = 3 {\left(\frac{4}{3}\right)}^{n}$