Answer
$k^{7/4}-k^{3/4}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the Distributive Property and the laws of exponents to simplify the given expression, $
k^{1/4} \left( k^{3/2}-k^{1/2} \right)
.$
$\bf{\text{Solution Details:}}$
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
k^{1/4}(k^{3/2})+k^{1/4}(-k^{1/2})
.\end{array}
Using the Product Rule of the laws of exponents which is given by $x^m\cdot x^n=x^{m+n},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
k^{\frac{1}{4}+{\frac{3}{2}}}-k^{\frac{1}{4}+\frac{1}{2}}
.\end{array}
Changing the rational exponents to similar fractions results to
\begin{array}{l}\require{cancel}
k^{\frac{1}{4}+{\frac{6}{4}}}-k^{\frac{1}{4}+\frac{2}{4}}
\\\\=
k^{\frac{7}{4}}-k^{\frac{3}{4}}
\\\\=
k^{7/4}-k^{3/4}
.\end{array}
