Explaining Variables and Terms Practice Questions

To review these concepts, go to Explaining Variables and Terms Study Guide.

Explaining Variables and Terms Practice Questions

Practice

Practice 1

For each problem, write the number of terms and list the variables.

1. x – 6
2. a + b
3. 3f + g
4. 5p + 6q – 7r
5. xy + 2z

Practice 2

For each term, find the coefficient, the base, and the exponent.

1. 5x³
2. z⁵
3. 
4. 8m
5. 

Practice 3

Label each pair of terms as "like" or "unlike."

1. 3p and 3q
2. –k⁶ and 12k⁶
3. and 8c²
4. 8m⁴ and 8n⁴
5. 5v¹⁰ and 3v^–10

Solutions

Practice 1

1. There are two terms, because x and 6 are separated by subtraction; x is the only variable.
2. There are two terms, because a and b are separated by addition; a and b are both letters, so they are both variables.
3. There are two terms, because 3f and g are separated by addition; f and g are both letters, so they are both variables.
4. There are three terms, because 5p and 6q are separated by addition and 6q and 7r are separated by subtraction; p, q, and r are all variables.
5. There are two terms, because xy and 2z are separated by addition; x, y, and z are all variables.

Practice 2

1. In the term 5x³, the number 5 multiplies x³, so 5 is the coefficient and x is the base. The exponent of the base is 3.
2. The term z⁵ has no number in front of z⁵, so the coefficient of the term is 1. The base is z and the exponent is 5.
3. The term can be rewritten . Since b is multiplied by , the coefficient of the term is and the base is b. b has no small number written above it and to the right, so it has an exponent of 1.
4. The term 8m has a coefficient of 8, a base of m, and an exponent of 1.
5. The term c⁷ has a coefficient of , since c⁷ is multiplied by . The base is c and the exponent is 7.

Practice 3

1. 3p and 3q have different bases, so they are unlike terms.
2. –k⁶ and 12k⁶ both have a base of k with an exponent of 6, so these terms are like terms.
3. and 8c² both have a base of c with an exponent of 2, so these terms are like terms.
4. 8m⁴ and 8n⁴ have the same exponent, but they have different bases, so they are unlike terms.
5. 5v¹⁰ and 3v^–10 both have a base of v, but the bases have different exponents, so they are unlike terms.