b) \$\\sqrt5{y^2}\$ c) \$\\sqrt7{z^2}\$

$b) \$\\sqrt5{y^2}\$ c) \$\\sqrt7{z^2}\$$

b) \$\sqrt5{y^2}\$ c) \$\sqrt7{z^2}\$

Recall that $\sqrt[n]{x^m} = x^{\frac{m}{n}}$. For $\sqrt[3]{y^2}$, $n=3$, $m=2$.
$\sqrt[3]{y^2} = y^{\frac{2}{3}}$

For $\sqrt[7]{z^2}$, $n=7$, $m=2$.
$\sqrt[7]{z^2} = z^{\frac{2}{7}}$

b) $y^{\frac{2}{3}}$
c) $z^{\frac{2}{7}}$