## Multiplying Monomials

Since a **monomial** is an algebraic expression, we can use the properties for simplifying expressions with exponents to multiply the monomials.

## Example

Multiply: \(\left(4{x}^{2}\right)\left(-5{x}^{3}\right).\)

### Solution

\(\left(4{x}^{2}\right)\left(-5{x}^{3}\right)\) | |

Use the Commutative Property to rearrange the factors. | \(4·\left(-5\right)·{x}^{2}·{x}^{3}\) |

Multiply. | \(-20{x}^{5}\) |

## Example

Multiply: \(\left(\frac{3}{4}\phantom{\rule{0.1em}{0ex}}{c}^{3}d\right)\left(12c{d}^{2}\right).\)

### Solution

\(\left(\frac{3}{4}\phantom{\rule{0.1em}{0ex}}{c}^{3}d\right)\left(12c{d}^{2}\right)\) | |

Use the Commutative Property to rearrange the factors. | \(\frac{3}{4}·12·{c}^{3}·c·d·{d}^{2}\) |

Multiply. | \(9{c}^{4}{d}^{3}\) |