$\begin{aligned} & \text { Given limit }=\lim _{n \rightarrow \infty}\left(4^n+5^n\right)^{1 / n} \\ & =\lim _{n \rightarrow \infty} 5\left[\left\{1+\left(\frac{4}{5}\right)^n\right\}^{(5 / 4)^n}\right]^{(1 / n) \cdot(4 / 5)^n}=5 \cdot e^0=5 . \\ & \left(\because\left(\frac{4}{5}\right)^n \rightarrow 0 \text { as } n \rightarrow \infty\right)\end{aligned}$