# 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 