Solve (8fg^{0}h^{7})(5fg^-3h)(7f^-3g^9h^-5)

$$( 8 f g ^ { 0 } h ^ { 7 } ) ( 5 f g ^ { - 3 } h ) ( 7 f ^ { - 3 } g ^ { 9 } h ^ { - 5 } )$$

Evaluate

$$\frac{280h^{3}g^{6}}{f}$$

Solution Steps

Multiply f and f to get f^{2}.

$$8f^{2}g^{0}h^{7}\times 5g^{-3}h\times 7f^{-3}g^{9}h^{-5}$$

To multiply powers of the same base, add their exponents. Add 2 and -3 to get -1.

$$8f^{-1}g^{0}h^{7}\times 5g^{-3}h\times 7g^{9}h^{-5}$$

To multiply powers of the same base, add their exponents. Add 0 and -3 to get -3.

$$8f^{-1}g^{-3}h^{7}\times 5h\times 7g^{9}h^{-5}$$

To multiply powers of the same base, add their exponents. Add -3 and 9 to get 6.

$$8f^{-1}g^{6}h^{7}\times 5h\times 7h^{-5}$$

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$8f^{-1}g^{6}h^{8}\times 5\times 7h^{-5}$$

To multiply powers of the same base, add their exponents. Add 8 and -5 to get 3.

$$8f^{-1}g^{6}h^{3}\times 5\times 7$$

Multiply 8 and 5 to get 40.

$$40f^{-1}g^{6}h^{3}\times 7$$

Multiply 40 and 7 to get 280.

$$280f^{-1}g^{6}h^{3}$$

Differentiate w.r.t. g

$$\frac{1680h^{3}g^{5}}{f}$$