Answer
$\sqrt{a}$
Work Step by Step
Using $\sqrt[n]{x^m}=(\sqrt[n]{x})^m=x^{m/n}$, the given expression, $
\sqrt[10]{a}\sqrt[5]{a^2}
,$ is equivalent to
\begin{array}{l}\require{cancel}
a^{\frac{1}{10}}\cdot a^{\frac{2}{5}}
.\end{array}
Using the least common denominator, 10, and the laws of exponents, the expression above simplifies to
\begin{array}{l}\require{cancel}
a^{\frac{1}{10}}\cdot a^{\frac{4}{10}}
\\\\=
a^{\frac{1}{10}+\frac{4}{10}}
\\\\=
a^{\frac{5}{10}}
\\\\=
a^{\frac{1}{2}}
\\\\=
\sqrt{a}
.\end{array}
