Answer
$\frac{\sqrt[5] {a^{2}b^{3}}}{2b^{3}}$
Work Step by Step
First we simplify the expression:
=$\frac{\sqrt[5] {a^{2}}}{\sqrt[5] {32b^{12}}}$
=$\frac{\sqrt[5] {a^{2}}}{\sqrt[5] {2^{5}\times b^{10+2}}}$
=$\frac{\sqrt[5] {a^{2}}}{\sqrt[5] {2^{5}\times b^{10}\times b^{2}}}$
=$\frac{\sqrt[5] {a^{2}}}{2b^{2}\times \sqrt[5] {b^{2}}}$
Next, we rationalize the denominator:
=$\frac{\sqrt[5] {a^{2}}}{2b^{2}\times \sqrt[5] {b^{2}}}\times\frac{ \sqrt[5] {b^{3}}}{ \sqrt[5] {b^{3}}}$
=$\frac{\sqrt[5] {a^{2}}\times\sqrt[5] {b^{3}}}{2b^{2}\times \sqrt[5] {b^{2}}\times\sqrt[5] {b^{3}}}$
=$\frac{\sqrt[5] {a^{2}b^{3}}}{2b^{2}\times \sqrt[5] {b^{5}}}$
=$\frac{\sqrt[5] {a^{2}b^{3}}}{2b^{2}\times b}$
=$\frac{\sqrt[5] {a^{2}b^{3}}}{2b^{3}}$
