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All sections of math are a building block and you have had years of building your math skills. As you now will be expanding to learning the beginnings of Algebra, it is always a good time to look back and see what you have learned. Exponents are a large part of Algebra. If you do not understand them and how they work, it will be very difficult to do algebraic math. So, to get you ready for your next phase of math, this quiz will be a review of how exponents work using simple addition and subtraction.

As you may recall, an exponent is that small superscript number that appears at the upper right-hand corner of a number.

As an example, if the number 6 is squared, it will look like 6^{2}. The “^{2}” is an exponent. What the exponent tells you is how many times a number is multiplied by itself. So, looking at our example 6^{2}, this tells you that 6 will be multiplied by itself two times or 6 x 6 and 6 x 6 = 36.

If we then have the number 6^{5}, we know the 6 will be multiplied by itself 5 times as follows:

6 x 6 x 6 x 6 x 6 =

6 x 6 = 36 x 6 = 216 x 6 = 1296 x 6 = 7776

Since it takes too long, and frankly too much space to write this out, math provides a shortcut by simply making it 6^{5}.

We then solve 6^{5} as follows: 6 x 6 = 36 x 6 = 216 x 6 = 1296 x 6 = 7776

__Adding and Subtracting__:

Understanding how the exponents work, we can now add and/or subtract numbers with exponents. Let’s look at the following practice problem to see how it is worked out to find a solution.

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

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

3 x 3 = 9

16 + 9 = 25

** Solution:** 2

1.

5^{4} + 11^{2} - 8^{3} =

85^{3}

18

234

512

2.

7^{2} + 4^{4} - 61 =

5

-31

144

244

7^{2} + 4^{4} - 61 =

7 x 7 = 49

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

49 + 256 = 305 - 61 = 244

__Solution__: 7^{2} + 4^{4} - 61 = __244__

Answer (d) is correct

7 x 7 = 49

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

49 + 256 = 305 - 61 = 244

Answer (d) is correct

3.

50^{2} - 25^{2} =

100

1875

2500

875

50^{2} - 25^{2} =

50 x 50 = 2500

25 x 25 = 625

2500 - 625 = 1875

__Solution__: 50^{2} - 25^{2} = __1875__

Answer (b) is correct

50 x 50 = 2500

25 x 25 = 625

2500 - 625 = 1875

Answer (b) is correct

4.

44 + 6^{2} - 3^{3} =

47^{5}

47

91

53

44 + 6^{2} - 3^{3} =

6 x 6 = 36

3 x 3 = 9 x 3 = 27

44 + 36 = 80 - 27 = 53

__Solution__: 44 + 6^{2} - 3^{3} = __53__

Answer (d) is correct

6 x 6 = 36

3 x 3 = 9 x 3 = 27

44 + 36 = 80 - 27 = 53

Answer (d) is correct

5.

7^{4} - 4^{5} =

3^{-1}

377

-28^{9}

1377

7^{4} - 4^{5} =

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

4 x 4 = 16 x 4 = 64 x 4 = 256 x 4 = 1024

2401 - 1024 = 1377

__Solution__: 7^{4} - 4^{5} = __1377__

Answer (d) is correct

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

4 x 4 = 16 x 4 = 64 x 4 = 256 x 4 = 1024

2401 - 1024 = 1377

Answer (d) is correct

6.

5^{3} + 8^{4} =

47

91

4221

422

5^{3} + 8^{4} =

5 x 5 = 25 x 5 = 125

8 x 8 = 64 x 8 = 512 x 8 = 4096

125 + 4096 = 4221

__Solution__: 5^{3} + 8^{4} = __4221__

Answer (c) is correct

5 x 5 = 25 x 5 = 125

8 x 8 = 64 x 8 = 512 x 8 = 4096

125 + 4096 = 4221

Answer (c) is correct

7.

24^{2} + 6^{2} =

60

612

60^{4}

30^{4}

24^{2} + 6^{2} =

24 x 24 = 576

6 x 6 = 36

576 + 36 = 612

__Solution__: 24^{2} + 6^{2} = __612__

Answer (b) is correct

24 x 24 = 576

6 x 6 = 36

576 + 36 = 612

Answer (b) is correct

8.

10^{3} + 20^{2} - 30^{2} =

500

0^{3}

-500

10

10^{3} + 20^{2} - 30^{2} =

10 x 10 = 100 x 10 = 1000

20 x 20 = 400

30 x 30 = 900

1000 + 400 = 1400 - 900 = 500

__Solution__: 10^{3} + 20^{2} - 30^{2} = __500__

Answer (a) is correct

10 x 10 = 100 x 10 = 1000

20 x 20 = 400

30 x 30 = 900

1000 + 400 = 1400 - 900 = 500

Answer (a) is correct

9.

26^{2} - 150 + 13^{3} =

41

513

2723

7223

26^{2} - 150 + 13^{3} =

26 x 26 = 676

13 x 13 = 169 x 13 = 2197

676 - 150 = 526 + 2197 = 2723

__Solution__: 26^{2} - 150 + 13^{3} = __2723__

Answer (c) is correct

26 x 26 = 676

13 x 13 = 169 x 13 = 2197

676 - 150 = 526 + 2197 = 2723

Answer (c) is correct

10.

9^{3} - 2^{4} + 162 =

875

1699^{7}

181

857

9^{3} - 2^{4} + 162 =

9 x 9 = 81 x 9 = 729

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

729 - 16 = 713 + 162 = 875

__Solution__: 9^{3} - 2^{4} + 162 = __875__

Answer (a) is correct

9 x 9 = 81 x 9 = 729

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

729 - 16 = 713 + 162 = 875

Answer (a) is correct

The next step is:

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^{4}+ 11^{2}- 8^{3}=5 x 5 = 25x 5 = 125 x 5 = 625

11 x 11 = 121

8 x 8 = 64 x 8 = 512

625 + 121 = 746 - 512 = 234

Solution: 5^{4}+ 11^{2}- 8^{3}=234Answer (c) is correct