Question

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

Answer 1

`=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`