# Chapter 10 - Section 10.5 - Rationalizing Numerators and Denominators of Radical Expressions - Practice: 5

$\frac{\sqrt[5] {a^{2}b^{3}}}{2b^{3}}$

#### 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: =$\frac{\sqrt[5] {a^{2}}}{2b^{2}\times \sqrt[5] {b^{2}}}\times\frac{ \sqrt[5] {b^{3}}}{ \sqrt[5] {b^{3}}}$ =$\frac{\sqrt[5] {a^{2}}\times\sqrt[5] {b^{3}}}{2b^{2}\times \sqrt[5] {b^{2}}\times\sqrt[5] {b^{3}}}$ =$\frac{\sqrt[5] {a^{2}b^{3}}}{2b^{2}\times \sqrt[5] {b^{5}}}$ =$\frac{\sqrt[5] {a^{2}b^{3}}}{2b^{2}\times b}$ =$\frac{\sqrt[5] {a^{2}b^{3}}}{2b^{3}}$

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