Solve frac{16x^{3}y^2}{6xz^4}*2yz^3/9y^4

$$\frac { 16 x ^ { 3 } y ^ { 2 } } { 6 x z ^ { 4 } } \cdot \frac { 2 y z ^ { 3 } } { 9 y ^ { 4 } }$$

Evaluate

$$\frac{16x^{2}}{27yz}$$

Solution Steps

Cancel out 2x in both numerator and denominator.

$$\frac{8x^{2}y^{2}}{3z^{4}}\times \frac{2yz^{3}}{9y^{4}}$$

Cancel out y in both numerator and denominator.

$$\frac{8x^{2}y^{2}}{3z^{4}}\times \frac{2z^{3}}{9y^{3}}$$

Multiply \frac{8x^{2}y^{2}}{3z^{4}} times \frac{2z^{3}}{9y^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8x^{2}y^{2}\times 2z^{3}}{3z^{4}\times 9y^{3}}$$

Cancel out y^{2}z^{3} in both numerator and denominator.

$$\frac{2\times 8x^{2}}{3\times 9yz}$$

Multiply 2 and 8 to get 16.

$$\frac{16x^{2}}{3\times 9yz}$$

Multiply 3 and 9 to get 27.

$$\frac{16x^{2}}{27yz}$$

Differentiate w.r.t. x

$$\frac{32x}{27yz}$$