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A monomial is one number that stands on its own such as the number 8 or 9*x* or 15*x*^{2}. To divide two monomials is really very easy. Let’s look at the following example.

25*x*^{3} ÷ 5*x*^{2}

Here we can easily divide 25 by 5 giving us the answer of 5. However, our variables *x*^{3} and *x*^{2} are different. So we need to break these out as follows:

*x*^{3} = *x*, *x*, *x*

*x*^{2} = *x*, *x*

Next you cross off a corresponding *x* from each variable. When you do this, it leaves one *x* left. This means the solution for our problem is: **25 x^{3} ÷ 5x^{2} = 5x**

1.

27*x*^{3} ÷ 9*x*^{4}

3*x*

3*x*^{7}

3*x*^{2}

3*x*^{12}

2.

10*x*^{6} ÷ 5*x*^{4}

50*x*^{10}

2*x*^{10}

50*x*^{22}

2*x*^{2}

10*x*^{6} ÷ 5*x*^{4}

10 ÷ 5 = 2

*x*^{6} = *x*, *x*, *x*, *x*, *x*, *x*

*x*^{4} = *x*, *x*, *x*, *x*

10*x*^{6} ÷ 5*x*^{4} = 2*x*^{2}

__Solution__: 2*x*^{2}

Answer (d) is the correct solution

10 ÷ 5 = 2

10

Answer (d) is the correct solution

3.

42*x*^{7} ÷ 7*x*^{3}

6*x*^{3}

6*x*^{21}

6*x*^{4}

6*x*^{10}

42*x*^{7} ÷ 7*x*^{3}

42 ÷ 7 = 6

*x*^{7} = *x*, *x*, *x*, *x*, *x*, *x*, *x*

*x*^{3} = *x*, *x*, *x*

42*x*^{7} ÷ 7*x*^{3} = 6*x*^{4}

Solution: 6*x*^{4}

Answer (c) is the correct solution

42 ÷ 7 = 6

42

Solution: 6

Answer (c) is the correct solution

4.

36*x*^{7} ÷ 6*x*^{4}

6*x*

6*x*^{21}

6*x*^{3}

6*x*^{11}

36*x*^{7} ÷ 6*x*^{4}

36 ÷ 6 = 6

*x*^{7} = *x*, *x*, *x*, *x*, *x*, *x*, *x*

*x*^{4} = *x*, *x*, *x*, *x*

36*x*^{7} ÷ 6*x*^{4} = 6*x*^{3}

__Solution__: 6*x*^{3}

Answer (c) is the correct solution

36 ÷ 6 = 6

36

Answer (c) is the correct solution

5.

16*x*^{4} ÷ 4*x*

4*x*^{5}

4*x*^{4}

4*x*^{3}

4*x*

16*x*^{4} ÷ 4*x*

16 ÷ 4 = 4

*x*^{4} = *x*, *x*, *x*, *x*

*x* = *x*

16*x*^{4} ÷ 4 = 4*x*^{3}

__Solution__: 4*x*^{3}

Answer (c) is the correct solution

16 ÷ 4 = 4

16

Answer (c) is the correct solution

6.

6*x* ÷ 3*x*

2*x*

2

2*x*^{2}

0

6*x* ÷ 3*x*

6 ÷ 3 = 2

*x* = *x*

*x* = *x*

6*x* ÷ 3*x* = 2 (the “*x*” is cancelled out)

__Solution__: 2

Answer (b) is the correct solution

6 ÷ 3 = 2

6

Answer (b) is the correct solution

7.

45*x*^{5} ÷ 5*x*^{4}

9*x*^{9}

9*x*

9*x*^{20}

9*x*^{5}

45*x*^{5} ÷ 5*x*^{4}

45 ÷ 5 = 9

*x*^{5} = *x*, *x*, *x*, *x*, *x*

*x*^{4} = *x*, *x*, *x*, *x*

45*x*^{5} ÷ 5*x*^{4} = 9*x*

__Solution__: 9*x*

Answer (b) is the correct solution

45 ÷ 5 = 9

45

Answer (b) is the correct solution

8.

2*x*^{5} ÷ 2*x*^{4}

4*x*^{9}

4*x*

2*x*^{5} ÷ 2*x*^{4}

2 ÷ 2 = 1

*x*^{5} = *x*, *x*, *x*, *x*, *x*

*x*^{4} = *x*, *x*, *x*, *x*

2*x*^{5} ÷ 2*x*^{4} = *x*

__Solution__: *x*

Answer (b) is the correct solution

2 ÷ 2 = 1

2

Answer (b) is the correct solution

9.

54*x*^{4} ÷ 6*x*^{2}

9*x*^{2}

9*x*^{4}

9*x*^{6}

9*x*^{8}

54*x*^{4} ÷ 6*x*^{2}

54 ÷ 6 = 9

*x*^{4} = *x*, *x*, *x*, *x*

*x*^{2} = *x*, *x*

54*x*^{4} ÷ 6*x*^{2} = 9*x*^{2}

__Solution__: 9*x*^{2}

Answer (a) is the correct solution

54 ÷ 6 = 9

54

Answer (a) is the correct solution

10.

9*x*^{3} ÷ 3*x*^{2}

3*x*^{3}

3*x*^{5}

3*x*^{6}

3*x*

9*x*^{3} ÷ 3*x*^{2}

9 ÷ 3 = 3

*x*^{3} = *x*, *x*, *x*

*x*^{2} = *x*, *x*

9*x*^{3} ÷ 3*x*^{2} = 3*x*

__Solution__: 3*x*

Answer (d) is the correct solution

9 ÷ 3 = 3

9

Answer (d) is the correct solution

x^{3}÷ 9x^{4}27 ÷ 9 = 3

x^{3}=x,x,xx^{4}=x,x,x,x27

x^{3}÷ 9x^{4}= 3xSolution: 3xAnswer (a) is the correct solution