Answer
$\sqrt{a}$
Work Step by Step
Using $\sqrt[n]{x^m}=(\sqrt[n]{x})^m=x^{m/n}$, the given expression, $
\sqrt[3]{a}\sqrt[6]{a}
,$ is equivalent to
\begin{array}{l}\require{cancel}
a^{\frac{1}{3}}\cdot a^{\frac{1}{6}}
.\end{array}
Using the least common denominator, 6, and the laws of exponents, the expression above simplifies to
\begin{array}{l}\require{cancel}
a^{\frac{2}{6}}\cdot a^{\frac{1}{6}}
\\\\=
a^{\frac{2}{6}+\frac{1}{6}}
\\\\=
a^{\frac{3}{6}}
\\\\=
a^{\frac{1}{2}}
\\\\=
\sqrt{a}
.\end{array}
