Question

Power series representation for:
f(x) = (1+x^2)^(-2/3)

I know we're supposed to use the taylor series:
1/(1+x) = (summation) ((-1)^k) * (x^k) for |x| <1
but I'm not entirely sure what to do about the power (2/3) when you flip it.

Answer 1

What I have so far:
\[\sum_{k=0}^{\infty} (-1)^k \times x^{2k}\]

Answer 2

What do you mean about the power (-2/3) when you "flip it"?

Answer 3

I flipped the given equation to:
\[{1/(1+x^2)}^{2/3}\]