Solve 7v^{-5}v*2y^-1*6x^6y^-8x^-6

$$7 v ^ { - 5 } v \cdot 2 y ^ { - 1 } \cdot 6 x ^ { 6 } y ^ { - 8 } x ^ { - 6 }$$

Evaluate

$$\frac{84}{v^{4}y^{9}}$$

Solution Steps

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

$$7v^{-4}\times 2y^{-1}\times 6x^{6}y^{-8}x^{-6}$$

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

$$7v^{-4}\times 2y^{-9}\times 6x^{6}x^{-6}$$

Multiply x^{6} and x^{-6} to get 1.

$$7v^{-4}\times 2y^{-9}\times 6$$

Multiply 7 and 2 to get 14.

$$14v^{-4}y^{-9}\times 6$$

Multiply 14 and 6 to get 84.

$$84v^{-4}y^{-9}$$

Differentiate w.r.t. y

$$-\frac{756}{v^{4}y^{10}}$$