Determine whether the given expression is a monomial. Write yes or no.

Explain your reasoning.

$3a^4$

A polynomial which contains only one non-zero single term is called a monomial. A monomial consists either one variable or a constant or products of more than one variable with a coefficient along with the exponents as a whole numbers.

Note: A monomial cannot have a variable in the denominator.The variable in the denominator is considered as second term.

The different parts of the monomial expression are given as follows:

Coefficient:The number which is multiplied by the variable in the expression.

Variable: The alphabets present in the monomial expression are called as variables

Literal part: All the other parts except the coefficient, are called the literal part of the expression.

Degree:The sum of the powers of the variables in the expression is the degree of the expression.

Example:$5a^2{b}^3$is a monomial expression.

Here,see that the coefficient is 5.

Variables in the given expression are a andb.

$$\begin{gathered} \text{Degree\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}the\hspace{0.17em}\hspace{0.17em}monomial\hspace{0.17em}\hspace{0.17em}expression}=\text{\hspace{0.17em}degree\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}}a+\text{degree\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}}b \\ =2+3 \\ =5 \end{gathered}$$

The literal part of the expression is $a^2{b}^3$.

From the definition, a monomial expression must contain only one non-zero term.

The expression$3a^4$contains a constant 3 and a variable ‘a’.

By the definition of monomial, $3a^4$is considered as one single term where 3 is the coefficient and$a^4$ is the literal part.

Hence, $3a^4$is a monomial.