How does exponents work?

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When you raise a number to the power of an exponent, like 14 ^ 4 or 14 ^ 3.46, how does this work? As in how can I do this in math. I know how to do 14 ^ 4, which yould be 14 * 14 * 14 * 14, but then how would 14 ^ 3.46 work?

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14^3.46 = 14^3 * 14^0.46

You will need a calculator for the 14^0.46 part.

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No, not using a calculator, pure hand written math.

[Edited by - digital_phantom on May 22, 2005 5:06:13 PM]

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I looked at that website and it just confused me.
Doesn't anyone know?

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The 14.46 is quite simply, 1423/50, which is the 50th root of 1423, so unless you happen to have a computer for a brain, you're not going to be doing this by hand.

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That's interesting Tenchi Muyo fan. lol.
But on my side I have programming tools, so I will be able to do those calculations.

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Quote:
 Original post by digital_phantomThat's interesting Tenchi Muyo fan. lol.But on my side I have programming tools, so I will be able to do those calculations.

In other words, you're using a glorified calculator.

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yeap. but the only reason why I want to know this, is for pure knowledge.
I'm the type of person who always wants to know how something works.

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Well here is the taylor series of several exponential functions including the key one a^x you were looking for. However this introduces the new problem of calculating a logarithm by hand.

Check out this for info on how to get a logarithm.

There could be better resources and faster ways to get a decent value, but I don't know them, sorry. Hope this helps.

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