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

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

Evaluate

$$50u^{10}v^{12}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 9 and 1 to get 10.

$$2u^{10}w^{-3}w^{3}\times 5v^{9}\times 5v^{3}$$

Multiply w^{-3} and w^{3} to get 1.

$$2u^{10}\times 5v^{9}\times 5v^{3}$$

To multiply powers of the same base, add their exponents. Add 9 and 3 to get 12.

$$2u^{10}\times 5v^{12}\times 5$$

Multiply 2 and 5 to get 10.

$$10u^{10}v^{12}\times 5$$

Multiply 10 and 5 to get 50.

$$50u^{10}v^{12}$$

Differentiate w.r.t. u

$$500u^{9}v^{12}$$