How to use the binomial theorem to calculate binomials with a negative exponent I'm having some trouble with expanding a binomial when it is a fraction. eg $(a+b)^{-n}$ where $n$ is a positive integer and $a$ and $b$ are real numbers.
I've looked at several other answers on this site and around the rest of the web, but I can't get it to make sense. From what I could figure out from the Wikipedia page on the subject, $(a+b)^n$ where $n>0$
Any help will be much appreciated.

You will always get a series, and for my own part, I find the story easiest to understand when $a=1$. Then, the standard formula applies:
$$
(1+b)^t=1+tb+\frac{t(t-1)}2b^2+\sum_{k=3}^\infty\binom tkb^k\,,
$$
where $\binom tk=t(t-1)(t-2)\cdots (t-k+1)\big/k!$ . This is the Generalized Binomial Theorem mentioned in the comment of @Dr.MV, and it’s often proved in second-term Calculus. The formula is good and convergent whenever $|b|<1$, no matter whether $t$ is a negative integer or a rational number, or even a real number. When $a\ne1$, you’ll be mentioning $a^t$ everywhere. Note that this series expansion does not treat $a$ and $b$ symmetrically.
