Monomial Worksheets

Solutions

1Indicate which of the following expressions are monomials. If it is, indicate the degree and coefficient of the monomial. If it is not, state why it is not a monomial:

13x3

25x−3

33x + 1

4

5

6

7

2 Simplify:

12x2y3z + 3x2y3z

22x3 − 5x3 =

33x4 − 2x4 + 7x4 =

42 a2bc3 − 5a2bc3 + 3a2bc3 − 2 a2bc3 =

3Solve:

1(2x3) · (5x3) =

2(12x3) · (4x) =

35 · (2x2y3z) =

4(5x2y3z) · (2y2z2) =

5(18x3y2z5) · (6x3yz2) =

6(−2x3) · (−5x) · (−3x2) =

4 Solve:

1(12x3) : (4x) =

2(18x6y2z5) : (6x3yz2) =

3(36x3y7z4) : (12x2y2) =

4

5

6

5 Solve:

1(2x3)3 =

2(−3x2)3 =

3

1

Indicate which of the following expressions are monomials. If it is, indicate the degree and coefficient of the monomial. If it is not, state why it is not a monomial:

13x3

Degree: 3, coefficient: 3

2 5x−3

It is not a monomial because the exponent is not a natural number.

33x + 1

It is not a monomial because there is an addition.

4

Degree: 1, coefficient:

5

Degree: 4, coefficient:

6

It is not a monomial because it does not have a natural exponent.

7

It is not a monomial because the literal part is within a root.

2

Simplify:

12x2y3z + 3x2y3z = 5x2y3z

22x3 − 5x3 = −3x3

33x4 − 2x4 + 7x4 = 8x4

42a2bc3 − 5a2bc3 + 3a2bc3 − 2a2bc3 = −2a2bc3

3

Solve:

1(2x3) · (5x3) = 10x6

2(12x3) · (4x) = 48x4

35 · (2x2 y3z) = 10x2y3z

4(5x2y3z) · (2 y2z2) = 10x2y5z3

5(18x3y2z5) · (6x3yz2) = 108x6y3z7

6(−2x3) · (−5x) · (−3x2) = −30x6

4

Solve:

1(12x3) : (4x) = 3x2

2(18x6y2z5) : (6x3yz2 ) = 3x3yz3

3(36x3y7z4) : (12x2y2) = 3xy5z4

4

5 4x3y + 3x2y2 − 8x8

6

5

Solve:

1(2x3)3 = 23 · (x3)3 = 8x9

2(-3x2)3 = (-3)3 · (x3)2 = −27x6

3