Solve 75g^5h^6/8g^7h^4

$$\frac { 75 g ^ { 5 } h ^ { 6 } } { 8 g ^ { 7 } h ^ { 4 } }$$

Evaluate

$$\frac{75\times \left(\frac{h}{g}\right)^{2}}{8}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{75^{1}g^{5}h^{6}}{8^{1}g^{7}h^{4}}$$

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

$$\frac{75^{1}}{8^{1}}g^{5-7}h^{6-4}$$

Subtract 7 from 5.

$$\frac{75^{1}}{8^{1}}g^{-2}h^{6-4}$$

Subtract 4 from 6.

$$\frac{75^{1}}{8^{1}}\times \frac{1}{g^{2}}h^{2}$$

Divide 75 by 8.

$$\frac{75}{8}\times \frac{1}{g^{2}}h^{2}$$

Differentiate w.r.t. h

$$\frac{75h}{4g^{2}}$$