## College Algebra (11th Edition)

$-2^{1/2}my^{5/2}$
$\bf{\text{Solution Outline:}}$ Use the definition of rational exponents to convert the given expression, $-m\sqrt{2y^5} ,$ to exponential form. Then use the laws of exponents to simplify the resulting expression. $\bf{\text{Solution Details:}}$ Using the definition of rational exponents which is given by $a^{\frac{m}{n}}=\sqrt[n]{a^m}=\left(\sqrt[n]{a}\right)^m,$ the expression above is equivalent to \begin{array}{l}\require{cancel} -m\left( 2y^5 \right)^{\frac{1}{2}} .\end{array} Using the extended Power Rule of the laws of exponents which is given by $\left( x^my^n \right)^p=x^{mp}y^{np},$ the expression above is equivalent to \begin{array}{l}\require{cancel} -m\left( 2^{\frac{1}{2}}y^{5\left(\frac{1}{2}\right)} \right) \\\\= -m\left( 2^{\frac{1}{2}}y^{\frac{5}{2}} \right) \\\\= -2^{1/2}my^{5/2} .\end{array}