# How do you simplify 64(x^{4}y^{3})^{\frac{5}{6}}?

Jun 23, 2017

$64 {\left({x}^{4} {y}^{3}\right)}^{\frac{5}{6}} = 64 {x}^{3} {y}^{2} \sqrt[3]{x} \sqrt{y}$

#### Explanation:

Remember ${\left(a b\right)}^{m} = {a}^{m} {b}^{m}$ and ${\left({a}^{m}\right)}^{n} = {a}^{m n}$

Hence $64 {\left({x}^{4} {y}^{3}\right)}^{\frac{5}{6}}$

= $64 \times {\left({x}^{4}\right)}^{\frac{5}{6}} \times {\left({y}^{3}\right)}^{\frac{5}{6}}$

= $64 \times {x}^{4 \times \frac{5}{6}} \times {y}^{3 \times \frac{5}{6}}$

= $64 \times {x}^{\frac{20}{6}} \times {y}^{\frac{15}{6}}$

= $64 \times {x}^{\frac{\textcolor{red}{2} \times 10}{\textcolor{red}{2} \times 3}} \times {y}^{\frac{\textcolor{red}{3} \times 5}{\textcolor{red}{3} \times 2}}$

= $64 \times {x}^{\frac{10}{3}} \times {y}^{\frac{5}{2}}$

= $64 \times {x}^{3 + \frac{1}{3}} \times {y}^{2 + \frac{1}{2}}$

= $64 \times {x}^{3} {x}^{\frac{1}{3}} {y}^{2} {y}^{\frac{1}{2}}$

= $64 {x}^{3} {y}^{2} \sqrt[3]{x} \sqrt{y}$