Answer
$-8y^{2}+8y$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the Distributive Property and the laws of exponents to simplify the given expression, $
-8y^{11/7}(y^{3/7}-y^{-4/7})
.$
$\bf{\text{Solution Details:}}$
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
-8y^{11/7}(y^{3/7})-8y^{11/7}(-y^{-4/7})
.\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}
-8y^{\frac{11}{7}+\frac{3}{7}}+8y^{\frac{11}{7}+\left( -\frac{4}{7}\right)}
\\\\=
-8y^{\frac{11}{7}+\frac{3}{7}}+8y^{\frac{11}{7}-\frac{4}{7}}
\\\\=
-8y^{\frac{14}{7}}+8y^{\frac{7}{7}}
\\\\=
-8y^{2}+8y^{1}
\\\\=
-8y^{2}+8y
.\end{array}
