## Intermediate Algebra (12th Edition)

$3z^{5/4}+5z^{2}$
$\bf{\text{Solution Outline:}}$ Use the Distributive Property and the laws of exponents to simplify the given expression, $z^{5/8} \left( 3z^{5/8}+5z^{11/8} \right) .$ $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to \begin{array}{l}\require{cancel} z^{5/8}( 3z^{5/8})+z^{5/8}(5z^{11/8}) .\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} 3z^{\frac{5}{8}+{\frac{5}{8}}}+5z^{\frac{5}{8}+\frac{11}{8}} \\\\= 3z^{\frac{10}{8}}+5z^{\frac{16}{8}} \\\\= 3z^{\frac{5}{4}}+5z^{2} \\\\= 3z^{5/4}+5z^{2} .\end{array}