Solve 6u^6h^17/3u^5h^10

$$\frac { 6 u ^ { 6 } h ^ { 17 } } { 3 u ^ { 5 } h ^ { 10 } }$$

Evaluate

$$2uh^{7}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{6^{1}u^{6}h^{17}}{3^{1}u^{5}h^{10}}$$

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

$$\frac{6^{1}}{3^{1}}u^{6-5}h^{17-10}$$

Subtract 5 from 6.

$$\frac{6^{1}}{3^{1}}u^{1}h^{17-10}$$

Subtract 10 from 17.

$$\frac{6^{1}}{3^{1}}uh^{7}$$

Divide 6 by 3.

$$2uh^{7}$$

Differentiate w.r.t. h

$$14uh^{6}$$