Question 558782: I don't understand how to solve a fraction to a negative (whole number) exponent. Can you please explain it to me?
Found 2 solutions by stanbon, rapaljer:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! I don't understand how to solve a fraction to a negative (whole number) exponent. Can you please explain it to me?
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The "negative" in an exponent means "invert".
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Examples:
3^-2 = 1/(3^2) = 1/9
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16^(-3/2)
The 2 means take the square root.
The 3 means cube
The negative means invert
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You may perform these directions in ANY order:
Taking the square root you get:
4^(-3)
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Inverting you get: (1/4)^3
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Cubing you get: 1/64
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Cheers,
stan H.
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Answer by rapaljer(4671)  (Show Source):
You can put this solution on YOUR website! A fraction raised to a negative exponent, essentially means to INVERT the fraction.  means 
 means invert the fraction and square, like this  which is 25/9.
For a complete explanation of negative exponents with LOTS of examples and exercises, please see my website. To go to my website, use the easy-to-spell and easy-to-remember link www.mathinlivingcolor.com. At the very bottom of this page, there is a link that will take you to my Homepage.
Once you are on my Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "Basic Algebra", and look in "Chapter 2," for "Section 2.13 Laws of Exponents: Negative and Zero" for a complete, non-traditional explanation that my own students, before I retired, found a lot easier to understand than the published textbooks of that day. You should really like my MATH IN LIVING COLOR pages, where the most difficult problems are solved IN COLOR. In addition, I have a video of me teaching this topic before I retired.
Everything on the website is FREE. If you find something you really like, just print your own copy of it!!
If anyone needs to contact me, especially about the website, my Email address is rapaljer@seminolestate.edu. I'll be glad to help you find an explanation on my website to help you with your algebra topic!
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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