Solve (5/6a^mb^n)(-3/10ab^2c)

$$( \frac { 5 } { 6 } a ^ { m } b ^ { n } ) ( - \frac { 3 } { 10 } a b ^ { 2 } c )$$

Evaluate

$$-\frac{ca^{m+1}b^{n+2}}{4}$$

Steps Using Commutative Property of Multiplication

Multiply \frac{5}{6} and -\frac{3}{10} to get -\frac{1}{4}.

$$-\frac{1}{4}a^{m}b^{n}ab^{2}c$$

Use the rules of exponents to simplify the expression.

$$\left(-\frac{1}{4}\right)^{1}a^{m}b^{n}c^{1}a^{1}b^{2}$$

Use the Commutative Property of Multiplication.

$$\left(-\frac{1}{4}\right)^{1}c^{1}a^{m}a^{1}b^{n}b^{2}$$

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

$$\left(-\frac{1}{4}\right)^{1}c^{1}a^{m+1}b^{n+2}$$

Multiply -\frac{1}{4} times c.

$$\left(-\frac{c}{4}\right)a^{m+1}b^{n+2}$$

Differentiate w.r.t. b

$$-\frac{c\left(n+2\right)a^{m+1}b^{n+1}}{4}$$