How to determine if an expression is a monomial?

Determine whether each expression is a monomial. Write yes or no. Explain.

3m

5k^{5}

-a^{4}

-6.8k^{2}

5k

-a

-6.8k

All the expressions are monomials because they only use multiplication.

For example, the expression -6.8k^{2} only uses multiplication

-6.8k^{2} =

-6.8 * k * k

-6.8 * k * k

See the definition of monomials.

Determine whether each expression is a monomial. Write yes or no. Explain.

Example.

Is the expression a monomial?

124cd

Yes, it is a monomial. Only multiplication is used here.

Example.

Is the expression a monomial?

29h^{-2}

No, it is not a monomial. Why? It is because the exponent of the variable h is negative.

We can write

29h^{-2} =

29/h^{2}

29/h

We have got a division. But a monomial cannot contain a division by a variable.

Example.

Is the expression a monomial?

2^{-2}h^{2}

Yes, it is a monomial. Why? The exponent of the coefficient 2 is negative. The coefficient of a monomial can have negative exponent but its literal part cannot.

We can write

2^{-2}h^{2} =

(1/2^{2}) * h^{2} =

(1/4) * h^{2} =

0.25 * h^{2} = 0.25h^{2}

(1/2

(1/4) * h

0.25 * h

The 0.25h^{2} is a monomial. Determine its degree. The degree of the monomial 0.25h^{2} is two.

See how to determine degree of monomial.