Solve (x^-2u/3z^-3)(x^3z^-1)

$$( \frac { x ^ { - 2 } u } { 3 z ^ { - 3 } } ) ( x ^ { 3 } z ^ { - 1 } )$$

Evaluate

$$\frac{uxz^{2}}{3}$$

Solution Steps

Express \frac{x^{-2}u}{3z^{-3}}x^{3} as a single fraction.

$$\frac{x^{-2}ux^{3}}{3z^{-3}}z^{-1}$$

Express \frac{x^{-2}ux^{3}}{3z^{-3}}z^{-1} as a single fraction.

$$\frac{x^{-2}ux^{3}z^{-1}}{3z^{-3}}$$

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

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

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

$$\frac{x^{1}uz^{2}}{3}$$

Calculate x to the power of 1 and get x.

$$\frac{xuz^{2}}{3}$$

Differentiate w.r.t. x

$$\frac{uz^{2}}{3}$$