Solve 4u^{2}v^8*2vx^-8*4u^-9x^7

$$4 u ^ { 2 } v ^ { 8 } \cdot 2 v x ^ { - 8 } \cdot 4 u ^ { - 9 } x ^ { 7 }$$

Evaluate

$$\frac{32v^{9}}{xu^{7}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and -9 to get -7.

$$4u^{-7}v^{8}\times 2vx^{-8}\times 4x^{7}$$

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$4u^{-7}v^{9}\times 2x^{-8}\times 4x^{7}$$

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

$$4u^{-7}v^{9}\times 2x^{-1}\times 4$$

Multiply 4 and 2 to get 8.

$$8u^{-7}v^{9}x^{-1}\times 4$$

Multiply 8 and 4 to get 32.

$$32u^{-7}v^{9}x^{-1}$$

Differentiate w.r.t. x

$$-\frac{32v^{9}}{x^{2}u^{7}}$$