Solve 6y^{-8}*5xy^9*2v^5v^-3x^-3

$$6 y ^ { - 8 } \cdot 5 x y ^ { 9 } \cdot 2 v ^ { 5 } v ^ { - 3 } x ^ { - 3 }$$

Evaluate

$$60\times \left(\frac{v}{x}\right)^{2}y$$

Solution Steps

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

$$6y^{1}\times 5x\times 2v^{5}v^{-3}x^{-3}$$

To multiply powers of the same base, add their exponents. Add 1 and -3 to get -2.

$$6y^{1}\times 5x^{-2}\times 2v^{5}v^{-3}$$

To multiply powers of the same base, add their exponents. Add 5 and -3 to get 2.

$$6y^{1}\times 5x^{-2}\times 2v^{2}$$

Calculate y to the power of 1 and get y.

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

Multiply 6 and 5 to get 30.

$$30yx^{-2}\times 2v^{2}$$

Multiply 30 and 2 to get 60.

$$60yx^{-2}v^{2}$$

Differentiate w.r.t. x

$$-\frac{120yv^{2}}{x^{3}}$$