Answer
$a)$ $y^{3/2}$ or $\sqrt{y^{3}}$
$b)$ $10x^{7/12}$
Work Step by Step
$a)$ $\sqrt[6]{y^{5}}\sqrt[3]{y^{2}}$
Rewrite using rational exponents and evaluate the product:
$\sqrt[6]{y^{5}}\sqrt[3]{y^{2}}=y^{5/6}\cdot y^{2/3}=y^{3/2}$
$b)$ $(5\sqrt[3]{x})(2\sqrt[4]{x})$
Rewrite using rational exponents and evaluate the product:
$(5\sqrt[3]{x})(2\sqrt[4]{x})=(5x^{1/3})(2x^{1/4})=10x^{7/12}$
