1. **Problem statement:** Solve the equation $9^{4/3} = 3^n$ for $n$. 2. **Rewrite the bases:** Note that $9 = 3^2$, so the equation becomes $\left(3^2\right)^{4/3} = 3^n$. 3. **Simplify the left side using the power of a power rule:** $$\left(3^2\right)^{4/3} = 3^{2 \times \frac{4}{3}} = 3^{\frac{8}{3}}.$$ 4. **Set the exponents equal:** Since the bases are the same and nonzero, equate the exponents: $$\frac{8}{3} = n.$$ 5. **Final answer:** $$n = \frac{8}{3}.$$