Solve 4a^3b^2*-8a^6b

$$4 a ^ { 3 } b ^ { 2 } \cdot - 8 a ^ { 6 } b$$

Evaluate

$$-32b^{3}a^{9}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$4^{1}a^{3}b^{2}\left(-8\right)^{1}a^{6}b^{1}$$

Use the Commutative Property of Multiplication.

$$4^{1}\left(-8\right)^{1}a^{3}a^{6}b^{2}b^{1}$$

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

$$4^{1}\left(-8\right)^{1}a^{3+6}b^{2+1}$$

Add the exponents 3 and 6.

$$4^{1}\left(-8\right)^{1}a^{9}b^{2+1}$$

Add the exponents 2 and 1.

$$4^{1}\left(-8\right)^{1}a^{9}b^{3}$$

Multiply 4 times -8.

$$-32a^{9}b^{3}$$

Differentiate w.r.t. a

$$-288b^{3}a^{8}$$