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:

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