Solve g^{52}h^80*g^42h*g^-1h^-2

$$g ^ { 52 } h ^ { 80 } \cdot g ^ { 42 } h \cdot g ^ { - 1 } h ^ { - 2 }$$

Evaluate

$$h^{79}g^{93}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$g^{52}h^{80}g^{42}h^{1}h^{-2}\times \frac{1}{g}$$

Use the Commutative Property of Multiplication.

$$g^{52}h^{1}h^{80}h^{-2}g^{42}\times \frac{1}{g}$$

To multiply powers of the same base, add their exponents.

$$g^{52}h^{1}h^{80-2}g^{42-1}$$

Add the exponents 80 and -2.

$$g^{52}h^{1}h^{78}g^{42-1}$$

Add the exponents 42 and -1.

$$g^{52}h^{1}h^{78}g^{41}$$

Multiply g^{52} times h.

$$hg^{52}h^{78}g^{41}$$

Differentiate w.r.t. h

$$79h^{78}g^{93}$$