What is 8 x 8 x 8 x 8 x 8 ...?
Exponents - Review of Simple Addition and Subtraction
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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 62. 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 62, 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 65, 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 65.
We then solve 65 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.
24 + 32 =
2 x 2 = 4 x 2 = 8 x 2 = 16
3 x 3 = 9
16 + 9 = 25
Solution: 24 + 32 = 25
7 x 7 = 49
4 x 4 = 16 x 4 = 64 x 4 = 256
49 + 256 = 305 - 61 = 244
Solution: 72 + 44 - 61 = 244
Answer (d) is correct
5 x 5 = 25 x 5 = 125
8 x 8 = 64 x 8 = 512 x 8 = 4096
125 + 4096 = 4221
Solution: 53 + 84 = 4221
Answer (c) is correct
10 x 10 = 100 x 10 = 1000
20 x 20 = 400
30 x 30 = 900
1000 + 400 = 1400 - 900 = 500
Solution: 103 + 202 - 302 = 500
Answer (a) is correct
50 x 50 = 2500
25 x 25 = 625
2500 - 625 = 1875
Solution: 502 - 252 = 1875
Answer (b) is correct
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: 54 + 112 - 83 = 234
Answer (c) is correct
24 x 24 = 576
6 x 6 = 36
576 + 36 = 612
Solution: 242 + 62 = 612
Answer (b) is correct
26 x 26 = 676
13 x 13 = 169 x 13 = 2197
676 - 150 = 526 + 2197 = 2723
Solution: 262 - 150 + 133 = 2723
Answer (c) is correct
6 x 6 = 36
3 x 3 = 9 x 3 = 27
44 + 36 = 80 - 27 = 53
Solution: 44 + 62 - 33 = 53
Answer (d) is correct
9 x 9 = 81 x 9 = 729
2 x 2 = 4 x 2 = 8 x 2 = 16
729 - 16 = 713 + 162 = 875
Solution: 93 - 24 + 162 = 875
Answer (a) is correct
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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: 74 - 45 = 1377
Answer (d) is correct