\input amstex

$$\aligned
(a+b)^n&=\sum\limits_{k=0}^n\binom nk a^kb^{n-k}\\
\biggl(\root 4\of{a^2x}+\frac1{\root 6\of{ax^2}}\biggr)^{13}&=\sum\limits_{k=0}^{13}\binom {13}k\bigl((a^2x)^{\frac14}\bigr)^k\bigl((ax^2)^{-\frac16}\bigr)^{13-k}=\\
&=\sum\limits_{k=0}^{13}\binom{13}k\bigl a^{\frac k2-\frac{13-k}6}x^{\frac k4-\frac{13-k}3},
\endaligned
$$
\bye