Answer
$\sqrt[10]{y}$
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 rule (3) above to obtain:
$=\dfrac{y^{\frac{2}{5}}}{y^{\frac{3}{10}}}$
Use rule (2) above to obtain:
$=y^{\frac{2}{5}-\frac{3}{10}}$
Make the fractions similar using their LCD of $10$ to obtain:
$=y^{\frac{4}{10} - \frac{3}{10}}
\\=y^{\frac{4-3}{10}}
\\=y^{\frac{1}{10}}$
Use rule (1) above to obtain:
$=\sqrt[10]{y}$
