Simplify (6x^2y^2z^-4)(-2x^3yz^2)^2/(-4x^2y^5z^-2)(3xyz^3)

Answer 1

(6x²y²z^-4)(-2x³yz²)² / (-4x²y⁵z^-2)(3xyz^-3)

Alright, let's start by doing some factoring so that we can cancel out parts and make this easier to digest. Thankfully everything is multiplication and division, so that makes everything so much easier.

For example, we have in the numerator a 6, and denominator -4 and 3, so we can factor out a 2 and the 3 in the denominator to cancel out the 6 in the numerator:

(x²y²z^-4)(-2x³yz²)² / (-2x²y⁵z^-2)(xyz^-3)

We can factor out x²:

(y²z^-4)(-2x³yz²)² / (-2y⁵z^-2)(xyz^-3)

We can factor out y² and reduce the y⁵ to y³ in the denominator:

(z^-4)(-2x³yz²)² / (-2y³z^-2)(xyz^-3)

We can factor out z^-3 as well and reduce z^-4 to z^-1 in the numerator:

(z^-1)(-2x³yz²)² / (-2y³z^-2)(xy)

And let's factor out the remaining z^-1 as well and reduce z^-2 to z^-1 in the denominator:

(-2x³yz²)² / (-2y³z^-1)(xy)

Now let's write out what that squaring in the numerator means:

(-2x³yz²)(-2x³yz²) / (-2y³z^-1)(xy)

We can factor out a -2:

(x³yz²)(-2x³yz²) / (y³z^-1)(xy)

Factor out xy in the denominator:

(x²z²)(-2x³yz²) / (y³z^-1)

Factor out y in the numerator:

(x²z²)(-2x³z²) / (y²z^-1)

1/z^-1 is the same as z, so we can flip it to place it in the numerator:

z(x²z²)(-2x³z²) / (y²)

Multiplying the numerator out, we're given:

-2x⁵z⁵ / y² or -2x⁵y^-2z⁵