Directions: Find the degree of each monomial. 1. 6x³ -> ____ 2. -2a²b⁴ -> ____ 3. 5 -> ____ 4. -7m³n²p -> ____ 5. (1/3)xy² -> ____
Answer (1)
To find the degree of a monomial, you calculate the sum of the exponents of all its variables. Here is how you can determine the degree for each of the given monomials:
6 x 3
The monomial 6 x 3 has only one variable, x , and its power is 3. So, the degree of the monomial is 3.
− 2 a 2 b 4
The monomial − 2 a 2 b 4 has variables a and b with powers 2 and 4, respectively. You add these exponents together: 2 + 4 = 6 . Therefore, the degree of the monomial is 6.
5
The monomial 5 is a constant with no variables. By convention, the degree of a constant (non-zero) is 0.
− 7 m 3 n 2 p
In the monomial − 7 m 3 n 2 p , the variables m , n , and p have powers 3, 2, and 1, respectively. Add these exponents: 3 + 2 + 1 = 6 . So, the degree of the monomial is 6.
3 1 x y 2
The monomial 3 1 x y 2 has variables x and y with powers 1 and 2, respectively. Add these exponents: 1 + 2 = 3 . Thus, the degree of the monomial is 3.
I hope this explanation helps you understand how to determine the degree of each monomial.
