Elementary Algebra

$10n^{\frac{1}{4}}$
Recall the following rule: $a^{n}\cdot a^{m}=a^{n+m}$. Therefore, we obtain: $(5n^{\frac{3}{4}})(2n^{-\frac{1}{2}})$ $=(5\times2)(n^{\frac{3}{4}-\frac{1}{2}})$ $=(10)(n^{\frac{3-2}{4}})$ $=10n^{\frac{1}{4}}$