Is $7 x^{3}$ $7x^3$ a monomial?

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Answer 1 · 2015-06-13T12:20:11

Yes it is.

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

Monomial Examples:

$5 x$ $5x$ , $W$ $color(white)"W"$ $\frac{2}{3} a^{2}$ $2/3a^2$ , $W$ $color(white)"W"$ $4 x^{3} y^{2} z$ $4x^3y^2z$

Examples that may take some thought:

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

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

$7 \sqrt{3} x^{5}$ $7sqrt3 x^5$ , (It is ok for the constant to involve a root)

Not Monomials:

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

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

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

Is 7x37x^3 a monomial?