Find the coefficient of the term that doesn't have $x$ in the expansion of

$\left(\sqrt[4]{x}+\frac{1}{\sqrt[10]{x}}\right)^7.$

The answer is 21.

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Let $\binom{7}{n} x^{\frac{n}{4}} x^{\frac{7-n}{-10}}$ the term which has no $x$ so $\frac{n}{4}=\frac{7-n}{-10} \Rightarrow n=2$

$\therefore$ the coefficient is $\boxed{\binom{7}{2}=21}$