# How do you simplify ""^3sqrt{\frac{16x^5}{135y^4}}?

Mar 26, 2018

$\frac{2 x}{3 y} 3 \sqrt{\frac{2 {x}^{2}}{5 y}}$

#### Explanation:

$3 \sqrt{\frac{16 {x}^{5}}{135 {y}^{4}}}$

$\frac{2 x}{3 y} 3 \sqrt{\frac{2 {x}^{2}}{5 y}}$

Bc you can factor out a 2 from the cuberoot of 16 since $16 = {2}^{4}$ so ${2}^{3} \cdot {2}^{1}$ and you can factor a 3 out of the cuberoot of 135 since $135 = {3}^{3} \cdot {5}^{1}$

Rearrange all the powers and terms of the variables.

#### Explanation:

 root(3)((16x^5)/(135y^4))

 ((16x^5)^(1/3))/((135y^4)^(1/3))

 (2^(4/3)x^(5/3))/(3*5^(1/3)y^(4/3)

That's about as simplified as I can make it.