Solve (6a^6b^7)(-5a^5b^3)

$$( 6 a ^ { 6 } b ^ { 7 } ) ( - 5 a ^ { 5 } b ^ { 3 } )$$

Evaluate

$$-30b^{10}a^{11}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$6^{1}a^{6}b^{7}\left(-5\right)^{1}a^{5}b^{3}$$

Use the Commutative Property of Multiplication.

$$6^{1}\left(-5\right)^{1}a^{6}a^{5}b^{7}b^{3}$$

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

$$6^{1}\left(-5\right)^{1}a^{6+5}b^{7+3}$$

Add the exponents 6 and 5.

$$6^{1}\left(-5\right)^{1}a^{11}b^{7+3}$$

Add the exponents 7 and 3.

$$6^{1}\left(-5\right)^{1}a^{11}b^{10}$$

Multiply 6 times -5.

$$-30a^{11}b^{10}$$

Differentiate w.r.t. a

$$-330\left(ab\right)^{10}$$