Solve frac{6f^{2}y^{3}h^5}{54f^-2g^-5h^3}

$$\frac { 6 f ^ { 2 } y ^ { 3 } h ^ { 5 } } { 54 f ^ { - 2 } g ^ { - 5 } h ^ { 3 } }$$

Evaluate

$$\frac{h^{2}y^{3}f^{4}g^{5}}{9}$$

Solution Steps

Cancel out 6h^{3} in both numerator and denominator.

$$\frac{f^{2}h^{2}y^{3}}{9g^{-5}f^{-2}}$$

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

$$\frac{h^{2}y^{3}f^{4}}{9g^{-5}}$$

Differentiate w.r.t. g

$$\frac{5h^{2}y^{3}\left(fg\right)^{4}}{9}$$