Solve frac{-6x^{2}yz^{4}x(-3xyz^{0})^2}{2xyz^4x-4x^2y^3z}

$$\frac { - 6 x ^ { 2 } y z ^ { 4 } x ( - 3 x y z ^ { 0 } ) ^ { 2 } } { 2 x y z ^ { 4 } x - 4 x ^ { 2 } y ^ { 3 } z }$$

Evaluate

$$-\frac{27y^{2}\left(xz\right)^{3}}{z^{3}-2y^{2}}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{-6x^{3}yz^{4}\left(-3xyz^{0}\right)^{2}}{2xyz^{4}x-4x^{2}y^{3}z}$$

Multiply x and x to get x^{2}.

$$\frac{-6x^{3}yz^{4}\left(-3xyz^{0}\right)^{2}}{2x^{2}yz^{4}-4x^{2}y^{3}z}$$

Calculate z to the power of 0 and get 1.

$$\frac{-6x^{3}yz^{4}\left(-3xy\right)^{2}}{2x^{2}yz^{4}-4x^{2}y^{3}z}$$

Expand \left(-3xy\right)^{2}.

$$\frac{-6x^{3}yz^{4}\left(-3\right)^{2}x^{2}y^{2}}{2x^{2}yz^{4}-4x^{2}y^{3}z}$$

Calculate -3 to the power of 2 and get 9.

$$\frac{-6x^{3}yz^{4}\times 9x^{2}y^{2}}{2x^{2}yz^{4}-4x^{2}y^{3}z}$$

Multiply -6 and 9 to get -54.

$$\frac{-54x^{3}yz^{4}x^{2}y^{2}}{2x^{2}yz^{4}-4x^{2}y^{3}z}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{-54x^{5}yz^{4}y^{2}}{2x^{2}yz^{4}-4x^{2}y^{3}z}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{-54x^{5}y^{3}z^{4}}{2x^{2}yz^{4}-4x^{2}y^{3}z}$$

Factor the expressions that are not already factored.

$$\frac{-54y^{3}z^{4}x^{5}}{2yzx^{2}\left(-2y^{2}+z^{3}\right)}$$

Cancel out 2yzx^{2} in both numerator and denominator.

$$\frac{-27y^{2}x^{3}z^{3}}{-2y^{2}+z^{3}}$$

Expand

$$-\frac{27y^{2}\left(xz\right)^{3}}{z^{3}-2y^{2}}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{-6x^{3}yz^{4}\left(-3xyz^{0}\right)^{2}}{2xyz^{4}x-4x^{2}y^{3}z}$$

Multiply x and x to get x^{2}.

$$\frac{-6x^{3}yz^{4}\left(-3xyz^{0}\right)^{2}}{2x^{2}yz^{4}-4x^{2}y^{3}z}$$

Calculate z to the power of 0 and get 1.

$$\frac{-6x^{3}yz^{4}\left(-3xy\right)^{2}}{2x^{2}yz^{4}-4x^{2}y^{3}z}$$

Expand \left(-3xy\right)^{2}.

$$\frac{-6x^{3}yz^{4}\left(-3\right)^{2}x^{2}y^{2}}{2x^{2}yz^{4}-4x^{2}y^{3}z}$$

Calculate -3 to the power of 2 and get 9.

$$\frac{-6x^{3}yz^{4}\times 9x^{2}y^{2}}{2x^{2}yz^{4}-4x^{2}y^{3}z}$$

Multiply -6 and 9 to get -54.

$$\frac{-54x^{3}yz^{4}x^{2}y^{2}}{2x^{2}yz^{4}-4x^{2}y^{3}z}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{-54x^{5}yz^{4}y^{2}}{2x^{2}yz^{4}-4x^{2}y^{3}z}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{-54x^{5}y^{3}z^{4}}{2x^{2}yz^{4}-4x^{2}y^{3}z}$$

Factor the expressions that are not already factored.

$$\frac{-54y^{3}z^{4}x^{5}}{2yzx^{2}\left(-2y^{2}+z^{3}\right)}$$

Cancel out 2yzx^{2} in both numerator and denominator.

$$\frac{-27y^{2}x^{3}z^{3}}{-2y^{2}+z^{3}}$$