Answer
$\dfrac{1}{p^{7/4}}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the laws of exponents to simplify the given expression, $
\dfrac{\left( p^{3}\right)^{1/4}}{\left( p^{5/4} \right)^{2}}
.$
$\bf{\text{Solution Details:}}$
Using the Power Rule of the laws of exponents which is given by $\left( x^m \right)^p=x^{mp},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{p^{3\cdot\frac{1}{4}}}{p^{\frac{5}{4}\cdot2}}
\\\\=
\dfrac{p^{\frac{3}{4}}}{p^{\frac{10}{4}}}
.\end{array}
Using the Quotient Rule of the laws of exponents which states that $\dfrac{x^m}{x^n}=x^{m-n},$ the expression above simplifies to
\begin{array}{l}\require{cancel}
p^{\frac{3}{4}-\frac{10}{4}}
\\\\=
p^{-\frac{7}{4}}
.\end{array}
Using the Negative Exponent Rule of the laws of exponents which states that $x^{-m}=\dfrac{1}{x^m}$ or $\dfrac{1}{x^{-m}}=x^m,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{1}{p^{\frac{7}{4}}}
\\\\=
\dfrac{1}{p^{7/4}}
.\end{array}
