Answer
a) $\sqrt[3] {10y}/2$
b) $\sqrt[3] {10y}/2$
c) There are multiple expressions by which the numerator and denominator can be rationalized and which result in the same result.
Work Step by Step
$\sqrt[3] {5y}\sqrt[3] {16}/(\sqrt[3] {4}\sqrt[3] {16})$
a)
$\sqrt[3] {5y}/\sqrt[3] {4}$
$(\sqrt[3] {5y})(\sqrt[3] {16})/(\sqrt[3] {4})(\sqrt[3] {16})$
$(\sqrt[3] {5*16y})/(\sqrt[3] {4*4*4})$
$(\sqrt[3] {80y})/4$
$(\sqrt[3] {8*10y})/4$
$(\sqrt[3] {2^3*10y})/4$
$(2*\sqrt[3] {10y})/4$
$\frac{1}{2}*\sqrt[3] {10y}$
b)
$(\sqrt[3] {5y})/(\sqrt[3] {4})$
$(\sqrt[3] {5y})(\sqrt[3] 2)/(\sqrt[3] {4})(\sqrt[3] 2)$
$(\sqrt[3] {5y*2})/(\sqrt[3] {4*2})$
$(\sqrt[3] {10y})/(\sqrt[3] {2*2*2})$
$\frac{1}{2}*\sqrt[3] {10y}$
