## Intermediate Algebra (12th Edition)

$-8y^{2}+8y$
$\bf{\text{Solution Outline:}}$ 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}