Simplify this index law question?

#((-2xy)^(2)*2(x^(2)y)^(3))/(8(xy)^(3))#

1 Answer
Tamir E.
Nov 16, 2017

#((-2xy)^2*2(x^2y)^3)/(8(xy)^3)=x^5y^2#

Explanation:

Laws:
#(x*y)^a=x^a*y^a#
#(x^a)^b=x^(a*b)#
#x^a*x^b=x^(a+b)#
#(x^a)/(x^b)=x^(a-b)#

#((-2xy)^2*2(x^2y)^3)/(8(xy)^3)#
#=((-2)^2x^2y^2*2x^(2*3)y^3)/(8x^3y^3)#
#=(4x^2y^2*2x^6y^3)/(8x^3y^3)#
#=((4*2)(x^2*x^6)(y^2*y^3))/(8x^3y^3)#
#=((8)(x^(2+6))(y^(2+3)))/(8x^3y^3)#
#=((8)(x^(8))(y^(5)))/(8x^3y^3)#
#=(8/8)((x^8)/(x^3))((y^5)/(y^3))#
#=(1)(x^(8-3))(y^(5-3))#
#=(x^(5))(y^(2))#
#=x^5y^2#

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