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

Aug 5, 2015

=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)))

$= \left(\textcolor{b l u e}{9 {x}^{6} {y}^{2}}\right) \cdot \left(- 64 {x}^{6} {y}^{12}\right)$

$= \left(- 9 \cdot 64\right) \left({x}^{6} \cdot {x}^{6}\right) \left({y}^{2} \cdot {y}^{12}\right)$

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

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

$= \left(- 9 \cdot 64\right) \left({x}^{\textcolor{b l u e}{6 + 6}}\right) \left({y}^{\textcolor{b l u e}{2 + 12}}\right)$

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