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# Explaining Variables and Terms Practice Questions

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Updated on Oct 3, 2011

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. 8m

#### 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.

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