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power to negative

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Manager
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power to negative [#permalink]

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New post 30 Jul 2008, 00:14
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Simple question... can't seem to figure this out.

2^-1=?
2^-2=?
2^-3=?
...
2^-n=?

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Re: power to negative [#permalink]

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New post 30 Jul 2008, 06:28
Do you undestand what a fraction in the exponent means ?

If you have \(4^{\frac{1}{2}} = \frac{1}{sqrt{4}} = \frac{1}{2}\)

Similarly:

\(4^{-\frac{1}{2}} = 2\) because \(4^{-\frac{1}{2}}=\frac{1}{4^{\frac{1}{2}}}= \frac{1}{(\frac{1}{sqrt{4}})} = \frac{1}{(\frac{1}{2})} = 2\)
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Re: power to negative [#permalink]

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New post 30 Jul 2008, 07:27
4^(1/3) is the 3rd root (cube root) of 4.

4^-3 = 1/4^3
4^-1/3 = 4^3
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Re: power to negative [#permalink]

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New post 30 Jul 2008, 08:18
Thanks all. Had a hard time remembering the rules for negative powers.

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Re: power to negative [#permalink]

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New post 30 Jul 2008, 09:13
jallenmorris wrote:
Do you undestand what a fraction in the exponent means ?

If you have \(4^{\frac{1}{2}} = \frac{1}{sqrt{4}} = \frac{1}{2}\)

Similarly:

\(4^{-\frac{1}{2}} = 2\) because \(4^{-\frac{1}{2}}=\frac{1}{4^{\frac{1}{2}}}= \frac{1}{(\frac{1}{sqrt{4}})} = \frac{1}{(\frac{1}{2})} = 2\)


As far as I know
If you have \(4^{\frac{1}{2}} = {sqrt{4}} = {2}\)

and as anything raised to negative power means inverse of the value with +ve power

\(4^{-\frac{1}{2}} = \frac{1}{sqrt{4}} = \frac{1}{2}\) if x not equal to zero

Rules:
only one rule: x^(-y) = \(1/(x^y)\)

Last edited by hi0parag on 30 Jul 2008, 09:15, edited 1 time in total.

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Re: power to negative [#permalink]

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New post 30 Jul 2008, 09:14
droopy57 wrote:
Simple question... can't seem to figure this out.

2^-1=?
2^-2=?
2^-3=?
...
2^-n=?


2^-1=1/2=0.5
2^-2=1/4=0.25
2^-3=1/8=0.125
...
2^-n=1/(2^n)

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Re: power to negative   [#permalink] 30 Jul 2008, 09:14
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