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Exponents, the numbers that tell how many times a base is multiplied by itself, are a part of mathematics that is not only very useful, but are a very short way of writing a multiplication question. There are exponent rules for different kinds of situations. In this report I hope to explain some of the more basic exponent rules. A Basic Exponent: When you have a basic exponent on a base, all this is telling you is to multiply the base number by itself the number of times the exponent tells it to. For example: 53 What this means is 5x5x5 (which equals 125) There is one exception to this rule: that anything to the power of zero equals one. For example: 30 = 1 Exponents on Fractions When you have a fraction with an exponent and the exponent is on the numerator, only the numerator is uses the exponent; the denominator stays the same. For example: 42 16 --- = --- 5 5 But when the fraction has a bracket around it, with the exponent outside the bracket, the exponent works on both the numerator and the denominator. For example:  The exponent of 2 works on the whole fraction. This equals: 9 --- 16 Order of Operations With Exponents In a calculation with exponents, you must do the exponent FIRST or you will get the answer wrong!!! For example: The Right Way 4 x 23 = 4 x 8 = 16 The Wrong Way 4 x 23 = 83 = 512 Exponents on Negative Numbers To multiply a number such as (- 5)2 you need to know how to multiply integers. When multiplying a sequence of numbers with negatives in them, first multiply the numbers without the negatives, then count the negatives. If the number of negatives is even, then the answer is positive. If the number of negatives is odd, the answer is negative. Some examples using the above rule: When you have a power like - 33 this says is that 3 is multiplied by itself three times, and there is only one negative, since the exponent is not in brackets. - 33 = - 3 x 3 x 3 = - 27 When the negative is in the brackets, all the numbers are negative: (-2)4 = -2 x -2 x -2 x -2 = 16 If there is a negative outside the bracket, the negative counts as another negative in the question. - (-3)4 = - -3 x -3 x -3 x -3 = - 81 because there are FIVE negative signs. If you have two different exponents, and the base is the same, all you do is add the exponents, and keep the base the same. 32 x 35 = 37 If the bases are different, then you have to work out each exponent separately, and multiply the answers. 23 x 32 = 8 x 9 = 72 Dividing Expressions with Exponents Again, to do this you need to be familiar with integer rules. To divide exponents like 53 / 52 you keep the base and subtract the exponents. 53 --- 52this equals 51 or 5 If the bases are different, the exponents need to be worked out first; then the answers can be divided. 23 --- 42the answer is 8/16, or 0.5 Negative Exponents When working out an expression that has a negative exponent, what you do is take the base, put it in a fraction with a numerator of one, keep the power on the base, but drop the negative. For example: 2-3 is equal to 1 --- 23which becomes 1 --- 8 There you have it ... most of the basic exponent rules for junior high math. |