Fractional exponent for binomial theorem

Question

If I am trying to expand $(a+b)^{\frac{2}{3}}$, can I use the binomial theorem like so: $$\sum_{k=0}^{\frac{2}{3}}{\frac{2}{3}\choose k}a^{\frac{2}{3}-k}b^k$$ or will that not work, since the last value of $k$ a fraction?

Answer 1

If $ \left|a\right|>\left|b\right| $, then we have : $$ \left(a+b\right)^{\frac{2}{3}}=\sum_{n=0}^{+\infty}{\binom{\frac{2}{3}}{n}a^{\frac{2}{3}-n}b^{n}} $$