Question

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

Answer 1

`(2x)/(3y) 3sqrt((2x^2)/(5y))`

Explanation:

`3sqrt((16x^5)/(135y^4))`

`(2x)/(3y) 3sqrt((2x^2)/(5y))`

Bc you can factor out a 2 from the cuberoot of 16 since `16=2^4` so `2^3 * 2^1` and you can factor a 3 out of the cuberoot of 135 since `135= 3^3 * 5^1`

Answer 2

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.