# Chapter 10 - Exponents and Radicals - 10.3 Multiplying Radical Expressions - 10.3 Exercise Set - Page 647: 51

$2xy^{2}\sqrt[4]{xy^3}$

#### Work Step by Step

Extracting the factors that are perfect roots of the given index, the given expression, $\sqrt[4]{16x^5y^{11}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[4]{16x^4y^{8}\cdot xy^3} \\\\= \sqrt[4]{(2xy^{2})^4\cdot xy^3} \\\\= 2xy^{2}\sqrt[4]{xy^3} \end{array} * Note that it is assumed that no radicands were formed by raising negative numbers to even powers.

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