Simplify this index law question?

((-2xy)^(2)*2(x^(2)y)^(3))/(8(xy)^(3))(2xy)22(x2y)38(xy)3

1 Answer
Nov 16, 2017

((-2xy)^2*2(x^2y)^3)/(8(xy)^3)=x^5y^2(2xy)22(x2y)38(xy)3=x5y2

Explanation:

Laws:
(x*y)^a=x^a*y^a(xy)a=xaya
(x^a)^b=x^(a*b)(xa)b=xab
x^a*x^b=x^(a+b)xaxb=xa+b
(x^a)/(x^b)=x^(a-b)xaxb=xab


((-2xy)^2*2(x^2y)^3)/(8(xy)^3)(2xy)22(x2y)38(xy)3
=((-2)^2x^2y^2*2x^(2*3)y^3)/(8x^3y^3)=(2)2x2y22x23y38x3y3
=(4x^2y^2*2x^6y^3)/(8x^3y^3)=4x2y22x6y38x3y3
=((4*2)(x^2*x^6)(y^2*y^3))/(8x^3y^3)=(42)(x2x6)(y2y3)8x3y3
=((8)(x^(2+6))(y^(2+3)))/(8x^3y^3)=(8)(x2+6)(y2+3)8x3y3
=((8)(x^(8))(y^(5)))/(8x^3y^3)=(8)(x8)(y5)8x3y3
=(8/8)((x^8)/(x^3))((y^5)/(y^3))=(88)(x8x3)(y5y3)
=(1)(x^(8-3))(y^(5-3))=(1)(x83)(y53)
=(x^(5))(y^(2))=(x5)(y2)
=x^5y^2=x5y2