# How do you fully simplify sqrt(x^15y^9)?

Nov 13, 2017

${x}^{7.5} {y}^{4.5}$ OR EQUIVALENTLY ${x}^{7} {y}^{4} \sqrt{x y}$

#### Explanation:

Start by rewriting the square root in an equivalent exponent form:

$\sqrt{{x}^{15} {y}^{9}} = {\left({x}^{15} {y}^{9}\right)}^{\frac{1}{2}}$

Use the power rule:

${\left({x}^{15} {y}^{9}\right)}^{\frac{1}{2}} = {x}^{7.5} {y}^{4.5}$

This could be considered simplest form, but if you did not want fractions in the exponents, you could rewrite this using the product rule:

$= {x}^{7} {x}^{0.5} {y}^{4} {y}^{0.5} = {x}^{7} \sqrt{x} {y}^{4} \sqrt{y} = {x}^{7} {y}^{4} \sqrt{x y}$