Solve frac{(-4yw^{2}t)*(-3xz^{2})*(-t^{2})}{(-xyzw^2t^3)*(-2z^2w^2)}

$$\frac { ( - 4 y w ^ { 2 } t ) \cdot ( - 3 x z ^ { 2 } ) \cdot ( - t ^ { 2 } ) } { ( - x y z w ^ { 2 } t ^ { 3 } ) \cdot ( - 2 z ^ { 2 } w ^ { 2 } ) }$$

Evaluate

$$-\frac{6}{zw^{2}}$$

Short Solution Steps

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

$$\frac{-4yw^{2}t\left(-3\right)xz^{2}\left(-t^{2}\right)}{\left(-x\right)yz^{3}w^{2}t^{3}\left(-2\right)w^{2}}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{-4yw^{2}t\left(-3\right)xz^{2}\left(-t^{2}\right)}{\left(-x\right)yz^{3}w^{4}t^{3}\left(-2\right)}$$

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

$$\frac{-3\left(-2\right)x\left(-t^{2}\right)}{-\left(-x\right)zt^{2}w^{2}}$$

Multiply -3 and -2 to get 6.

$$\frac{6x\left(-t^{2}\right)}{-\left(-x\right)zt^{2}w^{2}}$$

Multiply -1 and -1 to get 1.

$$\frac{6x\left(-t^{2}\right)}{xzt^{2}w^{2}}$$

Cancel out x in both numerator and denominator.

$$\frac{6\left(-t^{2}\right)}{zt^{2}w^{2}}$$

Factor the expressions that are not already factored.

$$\frac{-6t^{2}}{zt^{2}w^{2}}$$

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

$$\frac{-6}{zw^{2}}$$

Differentiate w.r.t. z

$$\frac{6}{\left(wz\right)^{2}}$$