Solve 5x^{-5}x^4uv^9*4u^6*4v^7

$$5 x ^ { - 5 } x ^ { 4 } u v ^ { 9 } \cdot 4 u ^ { 6 } \cdot 4 v ^ { 7 }$$

Evaluate

$$\frac{80u^{7}v^{16}}{x}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -5 and 4 to get -1.

$$5x^{-1}uv^{9}\times 4u^{6}\times 4v^{7}$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$5x^{-1}u^{7}v^{9}\times 4\times 4v^{7}$$

To multiply powers of the same base, add their exponents. Add 9 and 7 to get 16.

$$5x^{-1}u^{7}v^{16}\times 4\times 4$$

Multiply 5 and 4 to get 20.

$$20x^{-1}u^{7}v^{16}\times 4$$

Multiply 20 and 4 to get 80.

$$80x^{-1}u^{7}v^{16}$$

Differentiate w.r.t. x

$$-\frac{80u^{7}v^{16}}{x^{2}}$$