Solve 6v^{-3}w^-2*5w^5v^2*3u^8u

$$6 v ^ { - 3 } w ^ { - 2 } \cdot 5 w ^ { 5 } v ^ { 2 } \cdot 3 u ^ { 8 } u$$

Evaluate

$$\frac{90w^{3}u^{9}}{v}$$

Solution Steps

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

$$6v^{-1}w^{-2}\times 5w^{5}\times 3u^{8}u$$

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

$$6v^{-1}w^{3}\times 5\times 3u^{8}u$$

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$6v^{-1}w^{3}\times 5\times 3u^{9}$$

Multiply 6 and 5 to get 30.

$$30v^{-1}w^{3}\times 3u^{9}$$

Multiply 30 and 3 to get 90.

$$90v^{-1}w^{3}u^{9}$$

Differentiate w.r.t. v

$$-\frac{90w^{3}u^{9}}{v^{2}}$$