Easier Way to Evaluate PowersDate: 9/7/96 at 0:30:59 From: Randy Dority Subject: Easier Way to Evaluate Powers Do you know of any shortcuts to finding the answer to powers? Example: 7 to the 9th power = x Jonathan Date: 9/12/96 at 10:23:51 From: Doctor Jerry Subject: Re: Easier Way to Evaluate Powers While I'll mention one idea below, there are no real shortcuts to finding powers of numbers (without just doing it on a calculator). This is one reason that the invention of logarithms 400 years ago was thought to be such a time-saving invention. It saved many, many people a lot of time. I'll use the carat (^) notation for powers: 7 to the 9th power is 7^9. The calculation can be divided in various ways. For example, 7^9 = (7^3)^3 So, if you know or calculate 7^3 = 343, then 7^9 = 343*343*343 = 40,353,607. Or, 7^9 = (((7^2)^2)^2)*7 = ((49^2)^2)*7 = (2401^2)*7 = 5,764,801*7 = 40,353,607. I like the first way better. It seems easier. Here's another problem: 2^10 = (2^5)^2 = 32^2 = 1024. How would you do 8^5? -Doctor Jerry, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
Search the Dr. Math Library: |
[Privacy Policy] [Terms of Use]
Ask Dr. Math^{TM}
© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/dr.math/