Answer
$a.\quad s^{2/3}$
$b.\quad 12\cdot x^{4/3}$
$c.\quad 32y^{5/2}$
$d.\quad 4a^{2}$
Work Step by Step
Apply the key concept: $\sqrt[n]{a^{m}}=a^{m/n}$
$a.$
$\sqrt[3]{s^{2}}=s^{2/3}$
$b.$
$12\sqrt[3]{x^{4}}=12\cdot x^{4/3}$
$c.$
$\sqrt[2]{(4y)^{5}}=(4y)^{5/2}=4^{5/2}y^{5/2}=(2^{2})^{5/2}=2^{5}y^{5/2}=32y^{5/2}$
$d.$
Recognize that $256=2^{8}=4^{4}$
$\sqrt[4]{256a^{8}}=\sqrt[4]{4^{4}(a^{2})^{4}}=\sqrt[4]{(4a^{2})^{4}}=4a^{2}$
