Solve (1/3a^2b^3)*(-15a^2b^2)

$$( \frac { 1 } { 3 } a ^ { 2 } b ^ { 3 } ) \cdot ( - 15 a ^ { 2 } b ^ { 2 } )$$

Evaluate

$$-5a^{4}b^{5}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(\frac{1}{3}\right)^{1}a^{2}b^{3}\left(-15\right)^{1}a^{2}b^{2}$$

Use the Commutative Property of Multiplication.

$$\left(\frac{1}{3}\right)^{1}\left(-15\right)^{1}a^{2}a^{2}b^{3}b^{2}$$

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

$$\left(\frac{1}{3}\right)^{1}\left(-15\right)^{1}a^{2+2}b^{3+2}$$

Add the exponents 2 and 2.

$$\left(\frac{1}{3}\right)^{1}\left(-15\right)^{1}a^{4}b^{3+2}$$

Add the exponents 3 and 2.

$$\left(\frac{1}{3}\right)^{1}\left(-15\right)^{1}a^{4}b^{5}$$

Multiply \frac{1}{3} times -15.

$$-5a^{4}b^{5}$$

Differentiate w.r.t. a

$$-20a^{3}b^{5}$$