Solve frac{5g^{-7}h}{g^-1h^0*5g^-1h^7}

$$\frac { 5 g ^ { - 7 } h } { g ^ { - 1 } h ^ { 0 } \cdot 5 g ^ { - 1 } h ^ { 7 } }$$

Evaluate

$$\frac{1}{g^{5}h^{6}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -1 and -1 to get -2.

$$\frac{5g^{-7}h}{g^{-2}h^{0}\times 5h^{7}}$$

To multiply powers of the same base, add their exponents. Add 0 and 7 to get 7.

$$\frac{5g^{-7}h}{g^{-2}h^{7}\times 5}$$

Cancel out 5h in both numerator and denominator.

$$\frac{g^{-7}}{g^{-2}h^{6}}$$

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

$$\frac{1}{g^{5}h^{6}}$$

Differentiate w.r.t. h

$$-\frac{6}{g^{5}h^{7}}$$