Solve (2/3xy)(-3x^2y)(5x^4y^5)

$$( \frac { 2 } { 3 } x y ) ( - 3 x ^ { 2 } y ) ( 5 x ^ { 4 } y ^ { 5 } )$$

Evaluate

$$-10\left(xy\right)^{7}$$

Solution Steps

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

$$\frac{2}{3}x^{3}y\left(-3\right)y\times 5x^{4}y^{5}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{2}{3}x^{7}y\left(-3\right)y\times 5y^{5}$$

Multiply y and y to get y^{2}.

$$\frac{2}{3}x^{7}y^{2}\left(-3\right)\times 5y^{5}$$

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$\frac{2}{3}x^{7}y^{7}\left(-3\right)\times 5$$

Multiply \frac{2}{3} and -3 to get -2.

$$-2x^{7}y^{7}\times 5$$

Multiply -2 and 5 to get -10.

$$-10x^{7}y^{7}$$

Differentiate w.r.t. x

$$-70x^{6}y^{7}$$