Question

What is the radical form of the expression (2x^4y^5)^3/8

Answer 1

We are given expression:
`(2x^4y^5)^(3/8)`

Let us distribute 3/8 over exponents in parenthesis, we get

`(2^(3/8)x^(4* 3/8)y^(5* 3/8)) = (2^(3/8)x^(12/8)y^(15/8))`

`= (2^(3/8)x^{1(4)/(8)} y^{1(7)/(8)} )`

We can get x and y out of the radical because, we get whlole number 1 for x and y exponents for the mixed fractions.

So, we could write it as.

`(2^(3/8)x^{1(4)/(8)} y^{1(7)/(8)} ) = xy(2^{(3)/(8) }x^{(4)/(8)} y^{(7)/(8)} )`

Now, we could write inside expression of parenthesis in radical form.

`xy\sqrt[8]{2x^(3)x^4y^7}`