# Is 7x^3 a monomial?

Jun 13, 2015

Yes it is.

#### Explanation:

A monomial is a product of a constant and variables raised to non-negative whole number powers.

Monomial Examples:

$5 x$, $\textcolor{w h i t e}{\text{W}}$ $\frac{2}{3} {a}^{2}$, $\textcolor{w h i t e}{\text{W}}$ $4 {x}^{3} {y}^{2} z$

Examples that may take some thought:

$3$, (Sometimes we say that this is $3 {x}^{0}$, since ${x}^{0} = 1$ for all $x$ except $x = 0$)

$0$, (sometimes it is helpful to write this as $0 {x}^{2}$ or $0 t$)

$7 \sqrt{3} {x}^{5}$, (It is ok for the constant to involve a root)

Not Monomials:

$\frac{2}{x}$ (Monomials do not have variables in the denominator.)

$5 \sqrt{x}$ (Monomials do not have roots of the variables.)

$3 {x}^{2} + 7 x$ (This is a binomial.)