Answer
$\sqrt{y}$
Work Step by Step
RECALL:
(1) $\sqrt[n]{a} = a^{\frac{1}{n}}$
(2) $\dfrac{a^m}{a^n} = a^{m-n}$
(3) $\sqrt[n]{a^m} = a^{\frac{m}{n}}$
Use rules (1) and (3) above to obtain:
$=\dfrac{y^{\frac{2}{3}}}{y^{\frac{1}{6}}}$
Use rule (2) above to obtain:
$=y^{\frac{2}{3}-\frac{1}{6}}$
Make the fractions similar using their LCD of $6$ to obtain:
$=y^{\frac{4}{6} - \frac{1}{6}}
\\=y^{\frac{4-1}{6}}
\\=y^{\frac{3}{6}}
\\=y^{\frac{1}{2}}$
Use rule (1) above to obtain:
$=\sqrt{y}$
