Solve (6x^18y^10)(-3x^6y^22)

$$( 6 x ^ { 18 } y ^ { 10 } ) ( - 3 x ^ { 6 } y ^ { 22 } )$$

Evaluate

$$-18x^{24}y^{32}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$6^{1}x^{18}y^{10}\left(-3\right)^{1}x^{6}y^{22}$$

Use the Commutative Property of Multiplication.

$$6^{1}\left(-3\right)^{1}x^{18}x^{6}y^{10}y^{22}$$

To multiply powers of the same base, add their exponents.

$$6^{1}\left(-3\right)^{1}x^{18+6}y^{10+22}$$

Add the exponents 18 and 6.

$$6^{1}\left(-3\right)^{1}x^{24}y^{10+22}$$

Add the exponents 10 and 22.

$$6^{1}\left(-3\right)^{1}x^{24}y^{32}$$

Multiply 6 times -3.

$$-18x^{24}y^{32}$$

Differentiate w.r.t. x

$$-432x^{23}y^{32}$$