Answer
$y^{\frac{1}{2}}$
Work Step by Step
RECALL:
(i) $\sqrt[n]{a^m} = a^{\frac{m}{n}}$
(ii) $(a^m)^n=a^{mn}$
(iii) $a^m \cdot a^n = a^{m+n}$
Use rule (i) above to obtain:
$=\sqrt[3]{y\cdot y^{\frac{1}{2}}}$
Use rule {iii) to obtain:
$=\sqrt[3]{y^{1+\frac{1}{2}}}
\\=\sqrt[3]{y^{\frac{2}{2}+\frac{1}{2}}}
\\=\sqrt[3]{y^{\frac{3}{2}}}$
Use rule (i) to obtain:
$=(y^{\frac{3}{2}})^{\frac{1}{3}}$
Use rule (ii) above to obtain:
$=y^{\frac{3}{2}\cdot \frac{1}{3}}
\\=y^{\frac{3}{6}}
\\=y^{\frac{1}{2}}$
