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Explanation of Division with Exponents - Succeed in Algebra. Also refer to exponential, base, subtract, negative, mathematics, math, maths, Ron Kurtus, School for Champions. Copyright © Restrictions Division with Exponentsby Ron Kurtus (10 January 2008) When you divide two exponential numbers or variables with the same base, you subtract the exponents. When you divide an exponential number by itself, the exponent is 0. When you divided by a larger exponential with the same base, the exponent is negative. Questions you may have are:
This lesson will answer those questions. There is a mini-quiz near the end of the lesson. Subtract exponents in divisionWhen you divide exponential numbers or variables with the same base, you subtract the exponents. This can be demonstrated with the example of dividing 7*7*7*7*7 by 7*7. The result is:
Thus, you can see that 75/72 = 75-2 = 73. Likewise, x25/x10 = x25-10 = x15. If you have all variables, xy/xz = xy-z.
Dividing by itselfWhat happens when you divide an exponential number by itself? 113/113 = 113-3 = 110. The number 110 looks strange, but realizing that a number divided by itself equals 1, you can see that 110 = 1.
Negative exponentsBut what happens when you divide by a number that is larger? If you divide 53 by 57, you will get 53−7 = 5-4. But also, 5*5*5/5*5*5*5*5 = 1/5*5*5*5 = 1/54. Thus, 5-4 = 1/54. Likewise, x-3 = 1/x3.
SummaryYou subtract the exponents when dividing two exponential numbers or variables with the same base. When you divide an exponential number by itself, the exponent is 0. When you divided by a larger exponential with the same base, the exponent is negative. An exponential number with a negative exponent is the reciprocal of the exponential number. Increase your understanding by knowing the rules ResourcesThe following resources provide information on this subject: WebsitesBooksMiscellaneousMini-quiz to check your understanding1. What is the result of 253/25x? 2. What does x0/x0 equal? 3. What does 1/z-3 equal? If you got all three correct, you are on your way to becoming a Champion in Algebra. If you had problems, you had better look over the material again. What do you think?Do you have any questions, comments, or opinions on this subject? If so, send an email with your feedback. We will try to get back to you as soon as possible. Share linkFeel free to establish a link from your website to pages in this site. Or use our form to send this link to yourself or a friend. Students and researchersThe Web address of this page is Please include it as a reference in your report, document, or thesis. Where can you go from here?
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