Solve y^2z*z^2x/x^2y

$${ y }^{ 2 } z \times { z }^{ 2 } \frac{ x }{ { x }^{ 2 } y }$$

Evaluate

$$\frac{yz^{3}}{x}$$

Solution Steps

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

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

Cancel out x in both numerator and denominator.

$$y^{2}z^{3}\times \frac{1}{xy}$$

Express y^{2}\times \frac{1}{xy} as a single fraction.

$$\frac{y^{2}}{xy}z^{3}$$

Cancel out y in both numerator and denominator.

$$\frac{y}{x}z^{3}$$

Express \frac{y}{x}z^{3} as a single fraction.

$$\frac{yz^{3}}{x}$$

Differentiate w.r.t. x

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