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Question 673723: I am really struggling when the 'power' is either a fraction, a decimal or a square root. For example 5^1.9 or 4^square root of 6.
5^1 would be 5^2 would be 25, so logic would tell me since 1.9 is slightly less than 2, the number would be less than the 25, but I have no idea how to work these. I know in the other example the square root of 6 is 2.44, so that should tell me that it would be equal to 4^2.44, but again, while 4^2 is 16, I think the answer would be greater than that, but do not know how to do the math! All help would be tremendously appreciated. I have gone back to school after a 35 year absence and math is giving me problems.
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! Basically, the answer is that you follow the
normal rules that you know when dealing
with whole numbers.
You are right that it's hard to get a feel for
what something like  means,
but all you can do is apply rules that you know, like
(1)  and
(2)  and
(3) 
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You can always convert decimals to fractions, too, if it helps
 , and using rule (1) backwards,
You could do this on a calculator that only has +,-,x, and square root
like the one I'm using
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If you have  , follow rule (3)
Note that  , so you have
The 1000th root of 3 is probably a little more than 1, so
the fraction 1/1.0+ should be a little less than 1
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Hope some of this helps
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