Question

Write each monomial in standard form and name its coefficient.

Answer 1

The standard form is
`\boxed{3n^4m^2}` .

The coefficient is
`\boxed{3}`

Explanation:

What is Standard Form of Polynomial?

The standard form of a polynomial is a way of writing a polynomial such that the term with the highest power of the variables comes first followed by the other terms in decreasing order of the power of the variable

We are given the expression

`(2)/(3)m^2n \cdot 4.5 n^3\\\\`

and we have to convert to standard form

First multiply the constants together to get the coefficient:

`(2)/(3) \cdot 4.5 = (2 \cdot 4.5)/(3) = (9)/(3) = 3`

There is only one m term which is m²

Multiply the two n terms to get
`n \cdot n^3 = n^(1 + 3} = n^4`

Therefore in standard form we get ( in decreasing order of exponents)

`3n^4m^2`

The coefficient is 3