Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$x^{3}y^{5}$
Using the definition of rational exponents which is given by $a^{\frac{m}{n}}=\sqrt[n]{a^m}=\left(\sqrt[n]{a}\right)^m,$ the given expression is equivalent to \begin{array}{l}\require{cancel} \sqrt{x^6y^{10}} \\\\= \left( x^6y^{10} \right)^{1/2} .\end{array} Using the extended Power Rule of the laws of exponents which is given by $\left( x^my^n \right)^p=x^{mp}y^{np},$ the expression above is equivalent to \begin{array}{l}\require{cancel} \left( x^6y^{10} \right)^{1/2} \\\\= x^{6\cdot\frac{1}{2}}y^{10\cdot\frac{1}{2}} \\\\= x^{3}y^{5} .\end{array}