Solve 5u^{4}*2u^-3v*6w^9w^5v^-2

$$5 u ^ { 4 } \cdot 2 u ^ { - 3 } v \cdot 6 w ^ { 9 } w ^ { 5 } v ^ { - 2 }$$

Evaluate

$$\frac{60uw^{14}}{v}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and -3 to get 1.

$$5u^{1}\times 2v\times 6w^{9}w^{5}v^{-2}$$

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

$$5u^{1}\times 2v^{-1}\times 6w^{9}w^{5}$$

To multiply powers of the same base, add their exponents. Add 9 and 5 to get 14.

$$5u^{1}\times 2v^{-1}\times 6w^{14}$$

Calculate u to the power of 1 and get u.

$$5u\times 2v^{-1}\times 6w^{14}$$

Multiply 5 and 2 to get 10.

$$10uv^{-1}\times 6w^{14}$$

Multiply 10 and 6 to get 60.

$$60uv^{-1}w^{14}$$

Differentiate w.r.t. v

$$-\frac{60uw^{14}}{v^{2}}$$