Negative exponents are actually a result of the division property of exponents which we already talked about in this chapt...
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Negative exponents

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Negative exponents

  1. 1. Negative exponents are actually a result of the division property of exponents which we already talked about in this chapter. But, for now, we'll focus on how to deal with them instead of why they exist.<br />Think of negative exponents as numbers that are misplaced. If the exponent is negative in the numerator, it's because it really belongs in the denominator. And, if it's negative in the denominator, then it really belonged in the numerator. So all we need to do is move it and flip the sign.<br />Examples:<br />1) 1/(3-2) = 1 * 32 = 1* 9 = 9<br />Here the negative exponent was in the denominator, so all we need to do is " pull" it up to the numerator and drop the negative. Whatever gets " pulled up" will get multiplied by what was already there.<br />2) (2-2) / 3 = 1/ [3 * (22)] = 1/ (3 * 4) = 1/12<br />Here the negative exponent was in the numerator, so all we need to do is " pull" it down to the denominator and drop the negative. Whatever gets " pulled " will get multiplied by what was already there...in this case, the 3.<br />3) (4-1) / (5-3) = (53) / (41) = 125 / 4<br />In this case  we have negative exponents in both spots. So we needed to move both numbers to opposite spots. Since there was only one number in both the numerator and denominator, when we 'switched' them a 1 was left...that's why there was no other number to multipy by.<br />4) 4-2 = 1/42 = 1/16<br />When there looks like there is just a whole number with a negative exponent, remember that ALL whole numbers can be written as a fraction by dividing by a (1). Also, when you 'move' a number and it's the only term there, a one takes it's place...not a zero!<br />

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