Answer
$-3\cdot5^{1/2}p^{3/2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the definition of rational exponents to convert the given expression, $
-3\sqrt{5p^3}
,$ 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}
-3\left( 5p^3 \right)^{\frac{1}{2}}
.\end{array}
Using the extended Power Rule of the laws of exponents which states that $\left( x^my^n \right)^p=x^{mp}y^{np},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
-3\left( 5^{\frac{1}{2}}p^{3\left(\frac{1}{2}\right)} \right)
\\\\=
-3\left( 5^{\frac{1}{2}}p^{\frac{3}{2}} \right)
\\\\=
-3\cdot5^{1/2}p^{3/2}
.\end{array}
