Solve 48u^8z^7/18u^2z^4

$$\frac { 48 u ^ { 8 } z ^ { 7 } } { 18 u ^ { 2 } z ^ { 4 } }$$

Evaluate

$$\frac{8z^{3}u^{6}}{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{48^{1}u^{8}z^{7}}{18^{1}u^{2}z^{4}}$$

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

$$\frac{48^{1}}{18^{1}}u^{8-2}z^{7-4}$$

Subtract 2 from 8.

$$\frac{48^{1}}{18^{1}}u^{6}z^{7-4}$$

Subtract 4 from 7.

$$\frac{48^{1}}{18^{1}}u^{6}z^{3}$$

Reduce the fraction \frac{48}{18} to lowest terms by extracting and canceling out 6.

$$\frac{8}{3}u^{6}z^{3}$$

Differentiate w.r.t. z

$$8z^{2}u^{6}$$