$$\begin{aligned} & T_{r+1}={ }^{15} \mathrm{C}_r\left(2^{1 / 5}\right)^{15-r}\left(5^{1 / 3}\right)^r \\ & ={ }^{15} C_r 5^{r / 3} 2^{\left(3-\frac{r}{5}\right)} \end{aligned}$$

For rational terms,

$$\frac{r}{3}$$ and $$\frac{r}{5}$$ must be integer

3 and 5 divide $$r \Rightarrow 15$$ divides $$r \Rightarrow r=0$$ and $$r=15$$

$${ }^{15} C_0 5^0 2^3+{ }^{15} C_{15} 5^5 2^{(0)}$$

$$\begin{aligned} & =8+3125 \\ & =3133 \end{aligned}$$