Solve frac{v^{-2}w^5*v^5w^-1}{vw^-2}

$$\frac { v ^ { - 2 } w ^ { 5 } \cdot v ^ { 5 } w ^ { - 1 } } { v w ^ { - 2 } }$$

Evaluate

$$v^{2}w^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -2 and 5 to get 3.

$$\frac{v^{3}w^{5}w^{-1}}{vw^{-2}}$$

To multiply powers of the same base, add their exponents. Add 5 and -1 to get 4.

$$\frac{v^{3}w^{4}}{vw^{-2}}$$

Cancel out v in both numerator and denominator.

$$\frac{v^{2}w^{4}}{w^{-2}}$$

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

$$v^{2}w^{6}$$

Differentiate w.r.t. w

$$6v^{2}w^{5}$$