## Elementary Algebra

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