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An exponent tells you how many times a number is multiplied by itself. For example, if you have the number 3 and you want to multiply it by itself six times you could write it out as follows:

3 x 3 x 3 x 3 x 3 x 3 =

This can become too long to always write out so we use a shortcut using a superscript number. In this case the superscript number would be “6” because we want to multiply 3 times itself six times. To show this using a superscript it will look like:

3^{6}

3^{6} = 3 x 3 x 3 x 3 x 3 x 3

We then solve it as: 3 x 3 = 9 x 3 = 27 x 3 = 81 x 3 = 243 x 3 = 729

3^{6} = 729

We can then multiply and/or divide using exponents as follows:

2^{3} x 5^{2} =

2 x 2 = 4 x 2 = 8

5 x 5 = 25

8 x 25 = 200

2^{3} x 5^{2} = **200**

1.

6^{3} x 1^{5} =

90

14

216

221

2.

8^{3} ÷ 2^{5} =

128

16

2.4

2

8^{3} ÷ 2^{5} =

8 x 8 = 64 x 8 = 512

2 x 2 = 4 x 2 = 8 x 2 = 16 x 2 = 32

512 ÷ 32 = 16

8^{3} ÷ 2^{5} = **16**

8 x 8 = 64 x 8 = 512

2 x 2 = 4 x 2 = 8 x 2 = 16 x 2 = 32

512 ÷ 32 = 16

8

3.

40^{2} + 30^{2} ÷ 25 =

11.2

5.6

115

100

40^{2} + 30^{2} ÷ 25 =

40 x 40 = 1600

30 x 30 = 900

1600 + 900 = 2500 ÷ 25 = 100

40^{2} + 30^{2} ÷ 25 = **100**

40 x 40 = 1600

30 x 30 = 900

1600 + 900 = 2500 ÷ 25 = 100

40

4.

10^{3} ÷ 2^{3} =

8000

8.33

125

2

10^{3} ÷ 2^{3} =

10 x 10 = 100 x 10 = 1000

2 x 2 = 4 x 2 = 8

1000 ÷ 8 = 125

10^{3} ÷ 2^{3} = **125**

10 x 10 = 100 x 10 = 1000

2 x 2 = 4 x 2 = 8

1000 ÷ 8 = 125

10

5.

5^{5} ÷ 14^{2} =

-9

1.6

9.8

15.9

5^{5} ÷ 14^{2} =

5 x 5 = 25 x 5 = 125 x 5 = 625 x 5 = 3125

14 x 14 = 196

3125 ÷ 196 = 15.9

5^{5} ÷ 14^{2} = **15.9**

5 x 5 = 25 x 5 = 125 x 5 = 625 x 5 = 3125

14 x 14 = 196

3125 ÷ 196 = 15.9

5

6.

4^{4} x 4^{4} ÷ 4 =

64

16

16384

1024

4^{4} x 4^{4} ÷ 4 =

4 x 4 = 16 x 4 = 64 x 4 = 256

256 x 256 = 65536 ÷ 4 = 16384

4^{4} x 4^{4} ÷ 4 = **16384**

4 x 4 = 16 x 4 = 64 x 4 = 256

256 x 256 = 65536 ÷ 4 = 16384

4

7.

3^{3} x 6^{2} =

972

108

144

56

3^{3} x 6^{2} =

3 x 3 = 9 x 3 = 27

6 x 6 = 36

27 x 36 = 972

3^{3} x 6^{2} = **972**

3 x 3 = 9 x 3 = 27

6 x 6 = 36

27 x 36 = 972

3

8.

7^{3} x 2^{4} ÷ 16 =

343

10.5

2688

3.9

7^{3} x 2^{4} ÷ 16 =

7 x 7 = 49 x 7 = 343

2 x 2 = 4 x 2 = 8 x 2 = 16

343 x 16 = 5488 ÷ 16 = 343

7^{3} x 2^{4} ÷ 16 = **343**

7 x 7 = 49 x 7 = 343

2 x 2 = 4 x 2 = 8 x 2 = 16

343 x 16 = 5488 ÷ 16 = 343

7

9.

5^{2} x 2^{4} =

16

41

18

400

5^{2} x 2^{4} =

5 x 5 = 25

2 x 2 = 4 x 2 = 8 x 2 = 16

25 x 16 = 400

5^{2} x 2^{4} = **400**

5 x 5 = 25

2 x 2 = 4 x 2 = 8 x 2 = 16

25 x 16 = 400

5

10.

22^{2} x 9^{2} =

792

39204

396

8712

22^{2} x 9^{2} =

22 x 22 = 484

9 x 9 = 81

484 x 81 = 39204

22^{2} x 9^{2} = **39204**

22 x 22 = 484

9 x 9 = 81

484 x 81 = 39204

22

^{3}x 1^{5}=6 x 6 = 36 x 6 = 216

1 x 1 = 1 x 1 = 1 x 1 = 1 x 1 = 1

216 x 1 = 216

6

^{3}x 1^{5}=216