Answer
$-5x^{2}+5x$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the Distributive Property and the laws of exponents to simplify the given expression, $
-5x^{7/6}(x^{5/6}-x^{-1/6})
.$
$\bf{\text{Solution Details:}}$
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
-5x^{7/6}(x^{5/6})-5x^{7/6}(-x^{-1/6})
.\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}
-5x^{\frac{7}{6}+\frac{5}{6}}+5x^{\frac{7}{6}+\left(-\frac{1}{6} \right)}
\\\\=
-5x^{\frac{7}{6}+\frac{5}{6}}+5x^{\frac{7}{6}-\frac{1}{6}}
\\\\=
-5x^{\frac{12}{6}}+5x^{\frac{6}{6}}
\\\\=
-5x^{2}+5x^{1}
\\\\=
-5x^{2}+5x
.\end{array}
