Solve 5a^6b^3*(-4ab^8)

$$5 a ^ { 6 } b ^ { 3 } \cdot ( - 4 a b ^ { 8 } )$$

Evaluate

$$-20a^{7}b^{11}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$5^{1}a^{6}b^{3}\left(-4\right)^{1}a^{1}b^{8}$$

Use the Commutative Property of Multiplication.

$$5^{1}\left(-4\right)^{1}a^{6}a^{1}b^{3}b^{8}$$

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

$$5^{1}\left(-4\right)^{1}a^{6+1}b^{3+8}$$

Add the exponents 6 and 1.

$$5^{1}\left(-4\right)^{1}a^{7}b^{3+8}$$

Add the exponents 3 and 8.

$$5^{1}\left(-4\right)^{1}a^{7}b^{11}$$

Multiply 5 times -4.

$$-20a^{7}b^{11}$$

Differentiate w.r.t. a

$$-140a^{6}b^{11}$$