Solve 5x^2y/4z^4*12z^4x/y^3=

$$\frac { 5 x ^ { 2 } y } { 4 z ^ { 4 } } \times \frac { 12 z ^ { 4 } x } { y ^ { 3 } } =$$

Evaluate

$$\frac{15x^{3}}{y^{2}}$$

Solution Steps

Multiply \frac{5x^{2}y}{4z^{4}} times \frac{12z^{4}x}{y^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5x^{2}y\times 12z^{4}x}{4z^{4}y^{3}}$$

Cancel out 4yz^{4} in both numerator and denominator.

$$\frac{3\times 5xx^{2}}{y^{2}}$$

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

$$\frac{3\times 5x^{3}}{y^{2}}$$

Multiply 3 and 5 to get 15.

$$\frac{15x^{3}}{y^{2}}$$

Differentiate w.r.t. x

$$45\times \left(\frac{x}{y}\right)^{2}$$