Solve frac{-2x^{4}yz^{3}*9xyz^4}{(-6x)^2y^0z^7}

$$\frac { - 2 x ^ { 4 } y z ^ { 3 } \times 9 x y z ^ { 4 } } { ( - 6 x ) ^ { 2 } y ^ { 0 } z ^ { 7 } }$$

Evaluate

$$-\frac{y^{2}x^{3}}{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{-2x^{5}yz^{3}\times 9yz^{4}}{\left(-6x\right)^{2}y^{0}z^{7}}$$

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

$$\frac{-2x^{5}y^{2}z^{3}\times 9z^{4}}{\left(-6x\right)^{2}y^{0}z^{7}}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{-2x^{5}y^{2}z^{7}\times 9}{\left(-6x\right)^{2}y^{0}z^{7}}$$

Cancel out z^{7} in both numerator and denominator.

$$\frac{-2\times 9y^{2}x^{5}}{y^{0}\left(-6x\right)^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{-2\times 9y^{2}x^{5}}{\left(-6x\right)^{2}}$$

Multiply -2 and 9 to get -18.

$$\frac{-18y^{2}x^{5}}{\left(-6x\right)^{2}}$$

Expand \left(-6x\right)^{2}.

$$\frac{-18y^{2}x^{5}}{\left(-6\right)^{2}x^{2}}$$

Calculate -6 to the power of 2 and get 36.

$$\frac{-18y^{2}x^{5}}{36x^{2}}$$

Cancel out 18x^{2} in both numerator and denominator.

$$\frac{-y^{2}x^{3}}{2}$$

Differentiate w.r.t. x

$$-\frac{3\left(xy\right)^{2}}{2}$$