SOLUTION: 6^9 divided by 6^7

Question 558840: 6^9 divided by 6^7
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
The applicable rule is that if two terms have exponents and also have a common base (in this case the common base is 6) and you want to divide the terms you can do so by subtracting the exponent of the divisor from the exponent of the dividend to get the exponent of the common base for the quotient. (This is simpler to work than it sounds.)
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You are given 6^9 as the dividend and 6^7 as the divisor. So the answer is determined by the difference in the exponents. Namely the answer is obtained by raising 6 to the exponent (9 - 7) so that the answer is just 6^2.
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You can write things out to see why this is the case. For this problem, 6^9 is just 6 times itself 9 times or (6*6*6*6*6*6*6*6*6) and 6^7 is just 6 times itself 7 times or (6*6*6*6*6*6*6). You can do this division in fraction form as follows:
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and substitute the products for 6^9 and 6^7 as shown below:
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Now cross out all the 6's in the denominator with a corresponding 6 in the numerator:
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and you are left with just 6*6 or 6^2 in the numerator.
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I hope this helps you how to divide by subtracting exponents when you have terms with a common base.
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