Mathematics » Polynomials II » Use Multiplication Properties of Exponents

# Multiplying Monomials

## Multiplying Monomials

Since a monomial is an algebraic expression, we can use the properties of exponents to multiply monomials.

## Example

Multiply: $$\left(3{x}^{2}\right)\left(-4{x}^{3}\right).$$

### Solution

$$\begin{array}{cccc}& & & \hfill \left(3{x}^{2}\right)\left(-4{x}^{3}\right)\hfill \\ \text{Use the Commutative Property to rearrange the terms.}\hfill & & & \hfill 3·\left(-4\right)·{x}^{2}·{x}^{3}\hfill \\ \text{Multiply.}\hfill & & & \hfill -12{x}^{5}\hfill \end{array}$$

## Example

Multiply: $$\left(\frac{5}{6}{x}^{3}y\right)\left(12x{y}^{2}\right).$$

### Solution

$$\begin{array}{cccc}& & & \hfill \left(\frac{5}{6}{x}^{3}y\right)\left(12x{y}^{2}\right)\hfill \\ \text{Use the Commutative Property to rearrange the terms.}\hfill & & & \hfill \frac{5}{6}·12·{x}^{3}·x·y·{y}^{2}\hfill \\ \text{Multiply.}\hfill & & & \hfill 10{x}^{4}{y}^{3}\hfill \end{array}$$

### Optional Video:

You can watch the video below for additional instruction and practice with using multiplication properties of exponents: