Solve 1280v^9z^4/100v^3z^2

$$\frac { 1280 v ^ { 9 } z ^ { 4 } } { 100 v ^ { 3 } z ^ { 2 } }$$

Evaluate

$$\frac{64z^{2}v^{6}}{5}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{1280^{1}v^{9}z^{4}}{100^{1}v^{3}z^{2}}$$

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

$$\frac{1280^{1}}{100^{1}}v^{9-3}z^{4-2}$$

Subtract 3 from 9.

$$\frac{1280^{1}}{100^{1}}v^{6}z^{4-2}$$

Subtract 2 from 4.

$$\frac{1280^{1}}{100^{1}}v^{6}z^{2}$$

Reduce the fraction \frac{1280}{100} to lowest terms by extracting and canceling out 20.

$$\frac{64}{5}v^{6}z^{2}$$

Differentiate w.r.t. z

$$\frac{128zv^{6}}{5}$$