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

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

Evaluate

$$\frac{h^{2}g^{8}}{9}$$

Solution Steps

Cancel out 6f^{-2}h^{3} in both numerator and denominator.

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

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

$$\frac{h^{2}g^{8}}{9}$$

Differentiate w.r.t. g

$$\frac{8h^{2}g^{7}}{9}$$