How do you use laws of exponents to simplify #(3x^3y)^2(-4x^2y^4)^3#?

1 Answer
Aug 5, 2015

Answer:

#=color(blue)(-576* x^12* y^14#

Explanation:

#(3x^3y)^color(blue)(2) * (−4x^2y^4)^color(blue)(3#

  • As per property:
    #color(blue)((ab)^m =a^m * b^m#

Applying the same property to the expression,the exponents outside the brackets are multiplied with each of the terms within brackets.

#=(3^color(blue)(2)x^color(blue)((3*2))y^color(blue)(2)) * (−4^color(blue)(3)x^color(blue)((2*3))y^(4 *color(blue)(3)))#

#=(color(blue)(9x^6y^2)) * ( - 64x^6y^12)#

#=(-9*64) (x^6 *x^6) (y^2*y^12)#

  • As per property
    #color(blue)(a^m*a^n = a^(m+n)#

Applying the same to the exponents of #x# and #y#

#=(-9*64) (x^color(blue)(6+6)) (y^color(blue)(2 + 12))#

#=color(blue)(-576* x^12* y^14#