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

$$\frac{15}{22h^{3}}$$

Solution Steps

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

$$\frac{3h^{-7}g^{3}}{4h^{3}}\times \frac{10g^{-2}h^{5}}{11gh^{-2}}$$

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

$$\frac{3g^{3}}{4h^{10}}\times \frac{10g^{-2}h^{5}}{11gh^{-2}}$$

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

$$\frac{3g^{3}}{4h^{10}}\times \frac{10g^{-2}h^{7}}{11g}$$

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

$$\frac{3g^{3}}{4h^{10}}\times \frac{10h^{7}}{11g^{3}}$$

Multiply \frac{3g^{3}}{4h^{10}} times \frac{10h^{7}}{11g^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3g^{3}\times 10h^{7}}{4h^{10}\times 11g^{3}}$$

Cancel out 2g^{3}h^{7} in both numerator and denominator.

$$\frac{3\times 5}{2\times 11h^{3}}$$

Multiply 3 and 5 to get 15.

$$\frac{15}{2\times 11h^{3}}$$

Multiply 2 and 11 to get 22.

$$\frac{15}{22h^{3}}$$

Differentiate w.r.t. h

$$-\frac{45}{22h^{4}}$$