| Sometimes we need to multiply a number times itself, like: | |||
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2 × 2 = 4 |
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| And sometimes we need to multiply the number times itself a bunch of times: | |||
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2 × 2 × 2 × 2 × 2 = 32 |
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| If we multiply a bunch of a number it gets easy to make a mistake. | |||
| Math people wanted an quick way to write these down these problems. | |||
| They came up with a way that uses very little space | |||
| no matter how big the problem is. | |||
| What they do is write the number once. | |||
| Then they write down how many times the number gets multiplied. | |||
| So everybody knows which number means what. | |||
| It gets written like this: | |||
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25 means 2 × 2 × 2 × 2 × 2 |
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| The little number 5 up in the air is called an exponent. | |||
| In math talk, that means how many times you multiply the number times itself. | |||
| There's an easy mistake you can make | |||
| when you start to work with these exponent things. | |||
| That is to try to multiply the exponent. | |||
| To see this problem as 2 x 5. | |||
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NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! |
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| The exponent just tells you what to do. | |||
| It says: | |||
| Multiply the number to my left, TIMES ITSELF this many times. | |||
| So: | |||
| 21 = 2 | |||
| 24 = 2 × 2 × 2 × 2 = 16 | |||
| 210 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024 | |||
| WOW! exponents are really POWERFUL. | |||
| Take a 2 and a 10 and BINGO. You've got 1024! | |||
| Because of this, exponents are sometimes called powers. | |||
| If you have: | |||
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36 |
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| You would say "3 raised to the sixth power" | |||
| or just "3 to the sixth power" for short. | |||
| (Even 3 to the sixth for mega short) | |||
| Pop Quiz: | |||
| Does 3 6 mean 3 × 6? | |||
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NOT A CHANCE! |
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| It means: | |||
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3 × 3 × 3 × 3 × 3 × 3 = 729 |
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| The bad news is that there's no easy way to multiply six 3's together. | |||
| You multiply the first 2: 3 x 3 = 9. | |||
| Then multiply that by the third 3: 9 x 3 = 27 | |||
| and so on. | |||
| If you have a nice calculator, it might have a key like this: | |||
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| If it does, try getting the answer to 3 6 using these key punches: | |||
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| If that doesn't make the calculator come back with 729, | |||
| check the instructions. | |||
| Some calculators (especially some made by Hewlett Packard) | |||
| use a different key order. | |||
| OK, Review time: | |||
| 23 = 2 × 2 × 2 = 8 | |||
| 54 = 5 × 5 × 5 × 5 = 625 | |||
| 15 = 1 × 1 × 1 × 1 × 1 = 1 | |||
| 02 = 0 × 0 = 0 | |||
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copyright 2005 Bruce Kirkpatrick |
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