Is the Binomial Theorem extendable to other fields?

Question

I very well know that the Binomial Theorem can be extended from an integer power, to a rational exponent, any real number and perhaps to the complex field with $z^w=e^{w \cdot ln(z)}$ or $(x+iy)^{u+iv}=\bigl((x+iy)^{iv}\bigr)^u$. Is this theorem extendable to any other field $\mathbb F $ ?