Date: 11/07/2001 at 17:20:09 From: Alex Subject: Exponents Dear Dr. Math, I was sitting in math class today and I asked my teacher a question. She was not sure and told me to come to your Web site. Here's the question: Can you have exponents that are decimals? My teacher said that maybe they have it in the high math classes. Do you know? Respectfully, Alex, 6th grade
Date: 11/08/2001 at 14:45:57 From: Doctor Peterson Subject: Re: Exponents Hi, Alex. Good question! Your teacher is right; as you advance in math you will see more advanced kinds of exponents. When you first see exponents, only whole numbers are used. Then we introduce negative and zero exponents: n^0 (any number to zero power) - Dr. Math FAQ http://mathforum.org/dr.math/faq//faq.number.to.0power.html Zero as an Exponent - Dr. Math archives http://mathforum.org/dr.math/problems/gerleman2.1.96.html Briefly, for example, 2^-3 (that is, 2 to the -3 power) means the reciprocal of 2^3, which is 1/8. After that, we can talk about rational (fraction or decimal) exponents: Finding a Decimal Exponent http://mathforum.org/dr.math/problems/tyler3.21.98.html Resolving Decimal Exponents http://mathforum.org/dr.math/problems/adel.3.26.01.html Again briefly, 2^0.5, or 2^(1/2), the one-half power of 2, is the same as the square root of 2. You can see this by thinking about what the square of 2^(1/2) would be. Finally, we can talk about irrational exponents, like 2 raised to the pi power (and if you've ever heard of "imaginary numbers," we can use them, too): Meaning of Irrational Exponents http://mathforum.org/dr.math/problems/knobler.three.3.17.97.html This can't be explained briefly! Each step requires us to do a little new thinking, so it takes time to develop an understanding of all this. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.