Question

What is the degree of the monomial expressed as ${\text{x}}{{\text{y}}^2}{{\text{z}}^2}$?
Choose from the options given below.
$
  {\text{A}}{\text{. 3}} \\
  {\text{B}}{\text{. 4}} \\
  {\text{C}}{\text{. 5}} \\
  {\text{D}}{\text{. 6}} \\
$

Answer 1

Hint – In order to find the degree of the monomial, we consider the given term has one or more variables in it. Then we add the powers of all the variables in the monomial to find its degree. If a variable has no power written on its top, its power is equal to 1.

Complete step-by-step answer:
The degree of a term is generally the highest power of any variable in the term.
To find the degree of a monomial which has more than one variable, we take all the powers of the variables in the monomial, add them to get the degree.
Here the given monomial is ${\text{x}}{{\text{y}}^2}{{\text{z}}^2}$
It has 3 variables x, y and z where x has a power 1, y has a power 2 and z has a power 2.
(The power of a variable with nothing in its exponent place is 1)
Now the degree of the monomial is –
1 + 2 + 2 = 5

Therefore the degree of the monomial ${\text{x}}{{\text{y}}^2}{{\text{z}}^2}$is 5, or we can say ${\text{x}}{{\text{y}}^2}{{\text{z}}^2}$is a 5th degree monomial.
Option C is the correct answer.

Note – In order to solve this type of question the key is to know what means by a degree of a monomial. While calculating the degree of a monomial we do not take the scalar value before the variable into consideration, only the power of all the variables in the monomial matters.
The degree of a non-zero constant is zero.