Solve 2ab^2*-9a^3b^4

$$2a { b }^{ 2 } \times -9 { a }^{ 3 } { b }^{ 4 }$$

Evaluate

$$-18a^{4}b^{6}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$2^{1}a^{1}b^{2}\left(-9\right)^{1}a^{3}b^{4}$$

Use the Commutative Property of Multiplication.

$$2^{1}\left(-9\right)^{1}a^{1}a^{3}b^{2}b^{4}$$

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

$$2^{1}\left(-9\right)^{1}a^{1+3}b^{2+4}$$

Add the exponents 1 and 3.

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

Add the exponents 2 and 4.

$$2^{1}\left(-9\right)^{1}a^{4}b^{6}$$

Multiply 2 times -9.

$$-18a^{4}b^{6}$$

Differentiate w.r.t. a

$$-72a^{3}b^{6}$$