Solve 1280u^9x^4/100u^4x^2

$$\frac { 1280 u ^ { 9 } x ^ { 4 } } { 100 u ^ { 4 } x ^ { 2 } }$$

Evaluate

$$\frac{64x^{2}u^{5}}{5}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{1280^{1}u^{9}x^{4}}{100^{1}u^{4}x^{2}}$$

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

$$\frac{1280^{1}}{100^{1}}u^{9-4}x^{4-2}$$

Subtract 4 from 9.

$$\frac{1280^{1}}{100^{1}}u^{5}x^{4-2}$$

Subtract 2 from 4.

$$\frac{1280^{1}}{100^{1}}u^{5}x^{2}$$

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

$$\frac{64}{5}u^{5}x^{2}$$

Differentiate w.r.t. x

$$\frac{128xu^{5}}{5}$$