Answer
$-2^{1/2}my^{5/2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
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}
