Solve 1/2x^4y^2*(-2xy^3)*(-1/10x^3)

$$\frac { 1 } { 2 } x ^ { 4 } y ^ { 2 } \cdot ( - 2 x y ^ { 3 } ) \cdot ( - \frac { 1 } { 10 } x ^ { 3 } )$$

Evaluate

$$\frac{y^{5}x^{8}}{10}$$

Solution Steps

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

$$\frac{1}{2}x^{5}y^{2}\left(-2\right)y^{3}\left(-\frac{1}{10}\right)x^{3}$$

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$\frac{1}{2}x^{8}y^{2}\left(-2\right)y^{3}\left(-\frac{1}{10}\right)$$

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

$$\frac{1}{2}x^{8}y^{5}\left(-2\right)\left(-\frac{1}{10}\right)$$

Multiply \frac{1}{2} and -2 to get -1.

$$-x^{8}y^{5}\left(-\frac{1}{10}\right)$$

Multiply -1 and -\frac{1}{10} to get \frac{1}{10}.

$$\frac{1}{10}x^{8}y^{5}$$

Differentiate w.r.t. x

$$\frac{4y^{5}x^{7}}{5}$$