How do you simplify ((2^-1x^-3y^-1)(4x^-2)^0)/(2x^-4y^-3)^2?

1 Answer
Mar 18, 2018

(xy)^5/8

Explanation:

((2^-1x^-3y^-1)(4x^-2)^0)/(2x^-4y^-3)^2

We should first notice the power of 0. Anything to the power of 0 returns 1.

((2^-1x^-3y^-1)cancel((4x^-2)^0))/(2x^-4y^-3)^2

=>(2^-1x^-3y^-1)/(2x^-4y^-3)^2

Now, let's square all of the terms in the bottom:

(2^-1x^-3y^-1)/(2x^-4y^-3)^2

=>(2^-1x^-3y^-1)/(2^2x^-8y^-6)

Now we compare terms and combine like-terms:

(color(blue)(2^-1)color(red)(x^-3)color(orange)(y^-1))/(color(blue)(2^2)color(red)(x^-8)color(orange)(y^-6))

=>(color(red)(x^5)color(orange)(y^5))/(color(blue)(2^3))

We can finally simplify the way it is written:

(x^5y^5)/(2^3)

=>color(green)( (xy)^5/8)