How do you simplify [(xy^6)/(x^3y)]^-2[xy6x3y]2?

1 Answer
Mar 25, 2018

=> x^4/y^10x4y10

Explanation:

We start with:

=>[(xy^6)/(x^3y)]^-2[xy6x3y]2

We multiply all powers by -22:

=>(x^(-2)y^(6(-2)))/(x^(3(-2))y^(-2))x2y6(2)x3(2)y2

Simplifying powers:

=>(x^-2 y^-12)/(x^-6 y ^-2)x2y12x6y2

Division of terms with powers requires subtraction of powers:

=> x^(-2 - (-6)) y^(-12 - (-2))x2(6)y12(2)

Simplifying:

=>x^4y^-10x4y10

We can get rid of negative powers by moving yy to the denominator:

=> x^4/y^10x4y10