Solve (frac{3g^{5}h^{-7}}{4g^{2}h^3}).10g^-2h^5/11gh^-2

$$( \frac { 3 g ^ { 5 } h ^ { - 7 } } { 4 g ^ { 2 } h ^ { 3 } } ) . \frac { 10 g ^ { - 2 } h ^ { 5 } } { 11 g h ^ { - 2 } }$$

Evaluate

$$\frac{3g^{3}}{4h^{10}}$$

Solution Steps

Cancel out g^{2} in both numerator and denominator.

$$\frac{3h^{-7}g^{3}}{4h^{3}}$$

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

$$\frac{3g^{3}}{4h^{10}}$$

Differentiate w.r.t. h

$$-\frac{15g^{3}}{2h^{11}}$$