Solve 9v^{9}u*5w^-3*2u^2v^-10w^4

$$9 v ^ { 9 } u \cdot 5 w ^ { - 3 } \cdot 2 u ^ { 2 } v ^ { - 10 } w ^ { 4 }$$

Evaluate

$$\frac{90wu^{3}}{v}$$

Solution Steps

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

$$9v^{-1}u\times 5w^{-3}\times 2u^{2}w^{4}$$

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

$$9v^{-1}u^{3}\times 5w^{-3}\times 2w^{4}$$

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

$$9v^{-1}u^{3}\times 5w^{1}\times 2$$

Multiply 9 and 5 to get 45.

$$45v^{-1}u^{3}w^{1}\times 2$$

Calculate w to the power of 1 and get w.

$$45v^{-1}u^{3}w\times 2$$

Multiply 45 and 2 to get 90.

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

Differentiate w.r.t. w

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