Solve 3x^{10}w^-2w^2u*2x^-8*8u^-8

$$3 x ^ { 10 } w ^ { - 2 } w ^ { 2 } u \cdot 2 x ^ { - 8 } \cdot 8 u ^ { - 8 }$$

Evaluate

$$\frac{48x^{2}}{u^{7}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 10 and -8 to get 2.

$$3x^{2}w^{-2}w^{2}u\times 2\times 8u^{-8}$$

Multiply w^{-2} and w^{2} to get 1.

$$3x^{2}u\times 2\times 8u^{-8}$$

To multiply powers of the same base, add their exponents. Add 1 and -8 to get -7.

$$3x^{2}u^{-7}\times 2\times 8$$

Multiply 3 and 2 to get 6.

$$6x^{2}u^{-7}\times 8$$

Multiply 6 and 8 to get 48.

$$48x^{2}u^{-7}$$

Differentiate w.r.t. x

$$\frac{96x}{u^{7}}$$