Answer
$5^{\frac{2}{3}}$
Work Step by Step
Using laws of exponents, then,
\begin{array}{l}
5^{1/2}\cdot 5^{1/6}
\\\\=
5^{\frac{1}{2}+\frac{1}{6}}
\\\\=
5^{\frac{3}{6}+\frac{1}{6}}
\\\\=
5^{\frac{4}{6}}
\\\\=
5^{\frac{2}{3}}
.\end{array}
Intermediate Algebra (6th Edition)
by Martin-Gay, Elayn
Published by
Pearson
ISBN 10:
0321785045
ISBN 13:
978-0-32178-504-6
Chapter 7 - Section 7.2 - Rational Exponents - Exercise Set - Page 424: 46
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