#### Answer

$\sqrt[4]{27p^{3}}-\sqrt[3]{4x}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the definition of rational exponents to convert the given expression, $
(3p)^{3/4}-(4x)^{1/3}
,$ to radical 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}
\sqrt[4]{(3p)^{3}}-\sqrt[3]{(4x)^{1}}
.\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}
\sqrt[4]{3^3p^{3}}-\sqrt[3]{4^1x^{1}}
\\\\=
\sqrt[4]{27p^{3}}-\sqrt[3]{4x}
.\end{array}