Solve f^{0}g^{0}h^{-1}*fg^{-1}h^-1*f^0g^0h^7

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

Evaluate

$$\frac{fh^{5}}{g}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 0 and 1 to get 1.

$$f^{1}g^{0}h^{-1}g^{-1}h^{-1}f^{0}g^{0}h^{7}$$

To multiply powers of the same base, add their exponents. Add 1 and 0 to get 1.

$$f^{1}g^{0}h^{-1}g^{-1}h^{-1}g^{0}h^{7}$$

To multiply powers of the same base, add their exponents. Add 0 and -1 to get -1.

$$f^{1}g^{-1}h^{-1}h^{-1}g^{0}h^{7}$$

To multiply powers of the same base, add their exponents. Add -1 and 0 to get -1.

$$f^{1}g^{-1}h^{-1}h^{-1}h^{7}$$

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

$$f^{1}g^{-1}h^{-2}h^{7}$$

To multiply powers of the same base, add their exponents. Add -2 and 7 to get 5.

$$f^{1}g^{-1}h^{5}$$

Calculate f to the power of 1 and get f.

$$fg^{-1}h^{5}$$

Differentiate w.r.t. f

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