How do you simplify ((8x^2 y^(2/3))^(2/3)) /( 2(x^(3/4) y)^3)?

1 Answer
Sep 23, 2017

2/(x^(11/12)y^(23/9))

Explanation:

Here are some rules for simplification:

(x^a)^b = x^(ab)

x^a/x^b = x^(a-b)

x^a*x^b = x^(a+b)

x^(-n) = 1/(x^n)

Let us now simplify the numerator and denominator individually:

((8x^2y^(2/3))^(2/3)/(2(x^(3/4)y)^3)) = ((8^(2/3)*(x^(2*2/3))*(y^(2/3 ⋅2/3))))/(2⋅(x^(3/4*3))*(y^(1*3)))

=(4x^(4/3)y^(4/9))/(2x^(9/4)y^3) implies 2(x^(4/3 - 9/4))(y^(4/9 - 3))

= 2x^(-11/12)y^(-23/9) = 2/(x^(11/12)y^(23/9))