# Chapter 9 - Roots and Radicals - 9.2 - Simplifying Radicals - Problem Set 9.2 - Page 406: 46

$-32y^4\sqrt{5y}$

#### Work Step by Step

Using the properties of radicals, the given expression, $-8\sqrt{80y^9} ,$ simplifies to \begin{array}{l}\require{cancel} -8\sqrt{16y^8\cdot5y} \\\\= -8\sqrt{(4y^4)^2\cdot5y} \\\\= -8\cdot4y^4\sqrt{5y} \\\\= -32y^4\sqrt{5y} .\end{array} Note that all of the variables are assumed to represent non-negative real numbers.

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