Solve 3yv^{-9}*2y^-5v^8*5u^-3u^3

$$3 y v ^ { - 9 } \cdot 2 y ^ { - 5 } v ^ { 8 } \cdot 5 u ^ { - 3 } u ^ { 3 }$$

Evaluate

$$\frac{30}{vy^{4}}$$

Solution Steps

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

$$3y^{-4}v^{-9}\times 2v^{8}\times 5u^{-3}u^{3}$$

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

$$3y^{-4}v^{-1}\times 2\times 5u^{-3}u^{3}$$

Multiply u^{-3} and u^{3} to get 1.

$$3y^{-4}v^{-1}\times 2\times 5$$

Multiply 3 and 2 to get 6.

$$6y^{-4}v^{-1}\times 5$$

Multiply 6 and 5 to get 30.

$$30y^{-4}v^{-1}$$

Differentiate w.r.t. v

$$-\frac{30}{v^{2}y^{4}}$$