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An exponent is a small superscript number that tells you how many times a number is multiplied by itself. For example, if you have the number 4 and you want to multiply it by itself five times you could write it out as follows:

4 x 4 x 4 x 4 x 4 =

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 “5” because we want to multiply 4 times itself five times. To show this using a superscript it will look like:

4^{5}

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

We then solve it as: 4 x 4 = 16 x 4 = 64 x 4 = 256 x 4 = 1024

4^{5} = 1024

We can then add and/or subtract using exponents as follows:

32 + 73 =

3 x 3 = 9

7 x 7 = 49 x 7 = 343

9 + 343 = 352

32 + 73 = __352__

1.

12^{2} + 7^{5} =

16951

588

133

2545

2.

6^{3} + 5^{4} - 3^{5} =

88

598

589

53

6^{3} + 5^{4} - 3^{5} =

6 x 6 = 36 x 6 = 216

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

3 x 3 = 9 x 3 = 27 x 3 = 81 x 3 = 243

216 + 625 = 841 - 243= 598

6^{3} + 5^{4} - 3^{5} = **598**

Answer (b), therefore, shows the correct Order of Operation

6 x 6 = 36 x 6 = 216

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

3 x 3 = 9 x 3 = 27 x 3 = 81 x 3 = 243

216 + 625 = 841 - 243= 598

6

Answer (b), therefore, shows the correct Order of Operation

3.

28^{2} - 13^{2} =

953

615

60

82

28^{2} - 13^{2} =

28 x 28 = 784

13 x 13 = 169

784 - 169 = 615

28^{2} - 13^{2} = **615**

28 x 28 = 784

13 x 13 = 169

784 - 169 = 615

28

4.

2^{4} + 9^{3} =

35

745

77

113

2^{4} + 9^{3} =

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

9 x 9 = 81 x 9 = 729

16 + 729 = 745

2^{4} + 9^{3} = **745**

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

9 x 9 = 81 x 9 = 729

16 + 729 = 745

2

5.

10^{2} + 12^{3} - 9^{2} =

91

1909

1747

38

10^{2} + 12^{3} - 9^{2} =

10 x 10 = 100

12 x 12 = 144 x 12 = 1728

9 x 9 = 81

100 + 1728 = 1828 - 81 = 1747

10^{2} + 12^{3} - 9^{2} = **1747**

10 x 10 = 100

12 x 12 = 144 x 12 = 1728

9 x 9 = 81

100 + 1728 = 1828 - 81 = 1747

10

6.

10 + 4^{4} - 4^{3} =

202

330

70

14

10 + 4^{4} - 4^{3} =

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

4 x 4 = 16 x 4 = 64

10 + 256 = 266 - 64 = 202

10 + 4^{4} - 4^{3} = **202**

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

4 x 4 = 16 x 4 = 64

10 + 256 = 266 - 64 = 202

10 + 4

7.

8^{2} + 2^{3} - 14 =

58

8

36

54

8^{2} + 2^{3} - 14 =

8 x 8 = 64

2 x 2 = 4 x 2 = 8

64 + 8 = 72 - 14 = 58

8^{2} + 2^{3} - 14 = **58**

8 x 8 = 64

2 x 2 = 4 x 2 = 8

64 + 8 = 72 - 14 = 58

8

8.

100^{2} - 50^{2} + 17 =

268

12517

117

7517

100^{2} - 50^{2} + 17 =

100 x 100 = 10000

50 x 50 = 2500

10000 - 2500 = 7500 + 17 = 7517

100^{2} - 50^{2} + 17 = **7517**

100 x 100 = 10000

50 x 50 = 2500

10000 - 2500 = 7500 + 17 = 7517

100

9.

5^{3} + 6^{4} =

341

77

39

1421

5^{3} + 6^{4} =

5 x 5 = 25 x 5 = 125

6 x 6 = 36 x 6 = 216 x 6 = 1296

125 + 1296 = 1421

5^{3} + 6^{4} = **1421**

5 x 5 = 25 x 5 = 125

6 x 6 = 36 x 6 = 216 x 6 = 1296

125 + 1296 = 1421

5

10.

7^{3} + 3^{4} + 16 =

408

49

35

440

7^{3} + 3^{4} + 16 =

7 x 7 = 49 x 7 = 343

3 x 3 = 9 x 3 = 27 x 3 = 81

343 + 81 + 16 = 440

7^{3} + 3^{4} + 16 = **440**

7 x 7 = 49 x 7 = 343

3 x 3 = 9 x 3 = 27 x 3 = 81

343 + 81 + 16 = 440

7

The next step is:

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^{2}+ 7^{5}=12 x 12 = 144

7 x 7 = 49 x 7 = 343 x 7 = 2401 x 7 = 16807

144 + 16807 = 16951

12

^{2}+ 7^{5}=16951