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

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Answer 1 · 2017-09-23T02:35:05

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

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))#