Solve (xyz/x^2y)(x^4y^-2z/x^3yz)

$$( \frac { x y z } { x ^ { 2 } y } ) ( \frac { x ^ { 4 } y ^ { - 2 } z } { x ^ { 3 } y z } )$$

Evaluate

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

Solution Steps

Cancel out xy in both numerator and denominator.

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

Cancel out zx^{3} in both numerator and denominator.

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

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

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

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

$$\frac{zx}{xy^{3}}$$

Cancel out x in both numerator and denominator.

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

Differentiate w.r.t. z

$$\frac{1}{y^{3}}$$