Solve 6v^{-7}*5u^-7x^9x^-7v*3u^7

$$6 v ^ { - 7 } \cdot 5 u ^ { - 7 } x ^ { 9 } x ^ { - 7 } v \cdot 3 u ^ { 7 }$$

Evaluate

$$\frac{90x^{2}}{v^{6}}$$

Solution Steps

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

$$6v^{-6}\times 5u^{-7}x^{9}x^{-7}\times 3u^{7}$$

Multiply u^{-7} and u^{7} to get 1.

$$6v^{-6}\times 5x^{9}x^{-7}\times 3$$

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

$$6v^{-6}\times 5x^{2}\times 3$$

Multiply 6 and 5 to get 30.

$$30v^{-6}x^{2}\times 3$$

Multiply 30 and 3 to get 90.

$$90v^{-6}x^{2}$$

Differentiate w.r.t. x

$$\frac{180x}{v^{6}}$$