Solve frac{18xy^{3}z^2}{12x^2z}*7x^2yz/4v^3

$$\frac { 18 x y ^ { 3 } z ^ { 2 } } { 12 x ^ { 2 } z } \cdot \frac { 7 x ^ { 2 } y z } { 4 v ^ { 3 } }$$

Evaluate

$$\frac{21xz^{2}y^{4}}{8v^{3}}$$

Solution Steps

Cancel out 6xz in both numerator and denominator.

$$\frac{3zy^{3}}{2x}\times \frac{7x^{2}yz}{4v^{3}}$$

Multiply \frac{3zy^{3}}{2x} times \frac{7x^{2}yz}{4v^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3zy^{3}\times 7x^{2}yz}{2x\times 4v^{3}}$$

Cancel out x in both numerator and denominator.

$$\frac{3\times 7xyzzy^{3}}{2\times 4v^{3}}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{3\times 7xy^{4}zz}{2\times 4v^{3}}$$

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

$$\frac{3\times 7xy^{4}z^{2}}{2\times 4v^{3}}$$

Multiply 3 and 7 to get 21.

$$\frac{21xy^{4}z^{2}}{2\times 4v^{3}}$$

Multiply 2 and 4 to get 8.

$$\frac{21xy^{4}z^{2}}{8v^{3}}$$

Differentiate w.r.t. x

$$\frac{21z^{2}y^{4}}{8v^{3}}$$