| Let's say you had a nasty problem like this: | ||
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| Now maybe you know that: | ||
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| But with that exponent of 8 in there, things are not so simple. | ||
| A really nice trick with exponents and roots | ||
| is that when you have stuff like this, | ||
| you can do either the exponent first or the root first. | ||
| Do first whichever makes the problem easier. | ||
| It's your choice. | ||
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| So we can do ... | ||
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| and then do ... | ||
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38 = 6,561 |
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| Yeah, you probably need a calculator for that last part (at least I did!). | ||
| This little trick works both ways. | ||
| If we have: | ||
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| We can do the exponent first: | ||
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| Some people don't like the looks of the radical squiggle. | ||
| They think it looks too much like a division problem. | ||
| They wanted another way to write these. | ||
| Here it is. | ||
| A plain radical means the same as an exponent of one half. | ||
| That is: | ||
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| Radicals with numbers in them are the same as fraction exponents | ||
| with that number in the denominator (bottom part). | ||
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| AND ... Watch closely: | ||
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| SAY WHAT? | ||
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| Or, saying it another way: | ||
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| So if we had: | ||
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| With this fraction exponent trick | ||
| we can use all the rules we came up with for exponents. | ||
| Like the one about combining things with the same exponent. | ||
| If you read the exponent pages, | ||
| you might remember problems like this: | ||
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33 × 23 = (3 × 2)3 = 63 = 6 × 6 × 6 = 216 |
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| When we change roots to exponent fractions, we can do that too! | ||
| So, Change: | ||
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| To: | ||
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| 2 x 8 = 16, so we have: | ||
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| And this is still just a square root, so we can say: | ||
| "What times itself equals 16? | ||
| The answers are 4 and - 4. | ||
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copyright 2005 Bruce Kirkpatrick |
