Solve (2a^2b^3)(6a^-3b^-5)

$$( 2 a ^ { 2 } b ^ { 3 } ) ( 6 a ^ { - 3 } b ^ { - 5 } )$$

Evaluate

$$\frac{12}{ab^{2}}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$2^{1}a^{2}b^{3}\times 6^{1}a^{-3}b^{-5}$$

Use the Commutative Property of Multiplication.

$$2^{1}\times 6^{1}a^{2}a^{-3}b^{3}b^{-5}$$

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

$$2^{1}\times 6^{1}a^{2-3}b^{3-5}$$

Add the exponents 2 and -3.

$$2^{1}\times 6^{1}\times \frac{1}{a}b^{3-5}$$

Add the exponents 3 and -5.

$$2^{1}\times 6^{1}\times \frac{1}{a}b^{-2}$$

Multiply 2 times 6.

$$12\times \frac{1}{a}\times \frac{1}{b^{2}}$$

Differentiate w.r.t. a

$$-\frac{12}{\left(ab\right)^{2}}$$