## Intermediate Algebra (12th Edition)

$r^{\frac{11}{10}}+r^{\frac{27}{20}}$
$\bf{\text{Solution Outline:}}$ Use the Distributive Property and the laws of exponents to simplify the given expression, $r^{3/5} \left( r^{1/2}+r^{3/4} \right) .$ $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to \begin{array}{l}\require{cancel} r^{3/5} ( r^{1/2})+r^{3/5}(r^{3/4}) .\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} r^{\frac{3}{5}+{\frac{1}{2}}}+r^{\frac{3}{5}+\frac{3}{4}} .\end{array} Changing the rational exponents to similar fractions results to \begin{array}{l}\require{cancel} r^{\frac{6}{10}+{\frac{5}{10}}}+r^{\frac{12}{20}+\frac{15}{20}} \\\\= r^{\frac{11}{10}}+r^{\frac{27}{20}} .\end{array}