Solve (3x^{3}y^{6})(-2x^7y^2)(4x^7y^9)

$$( 3 x ^ { 3 } y ^ { 6 } ) ( - 2 x ^ { 7 } y ^ { 2 } ) ( 4 x ^ { 7 } y ^ { 9 } )$$

Evaluate

$$-24\left(xy\right)^{17}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 7 to get 10.

$$3x^{10}y^{6}\left(-2\right)y^{2}\times 4x^{7}y^{9}$$

To multiply powers of the same base, add their exponents. Add 10 and 7 to get 17.

$$3x^{17}y^{6}\left(-2\right)y^{2}\times 4y^{9}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$3x^{17}y^{8}\left(-2\right)\times 4y^{9}$$

To multiply powers of the same base, add their exponents. Add 8 and 9 to get 17.

$$3x^{17}y^{17}\left(-2\right)\times 4$$

Multiply 3 and -2 to get -6.

$$-6x^{17}y^{17}\times 4$$

Multiply -6 and 4 to get -24.

$$-24x^{17}y^{17}$$

Differentiate w.r.t. x

$$-408x^{16}y^{17}$$