Solve 2u^{-2}w^-3u^5*4x^-2*4w^4x

$$2 u ^ { - 2 } w ^ { - 3 } u ^ { 5 } \cdot 4 x ^ { - 2 } \cdot 4 w ^ { 4 } x$$

Evaluate

$$\frac{32wu^{3}}{x}$$

Solution Steps

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

$$2u^{3}w^{-3}\times 4x^{-2}\times 4w^{4}x$$

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

$$2u^{3}w^{1}\times 4x^{-2}\times 4x$$

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

$$2u^{3}w^{1}\times 4x^{-1}\times 4$$

Calculate w to the power of 1 and get w.

$$2u^{3}w\times 4x^{-1}\times 4$$

Multiply 2 and 4 to get 8.

$$8u^{3}wx^{-1}\times 4$$

Multiply 8 and 4 to get 32.

$$32u^{3}wx^{-1}$$

Differentiate w.r.t. x

$$-\frac{32wu^{3}}{x^{2}}$$