Developing in power series

Question

I would like to develop in power series $\frac{1}{(2+x)^3}$ and $ \frac{1}{(32-x)^{1/5}} $. What is the way to go ?

Thanks

Answer 1

Rewrite as $$\frac18\cdot\frac1{\Bigl(1-\dfrac x2\Bigr)^3}\quad\text{and}\quad\frac12\cdot\frac1{\Bigl(1-\dfrac x{32}\Bigr)^{1/5}},$$ and use the binomial formula.