1123581321 Posted February 13, 2011 Share Posted February 13, 2011 Would someone be able to please explain to me what the following means - a^-1 = 1/a, a^-m = 1/a^m I've recently gone over the area of scientific notation and this part in particular didn't make sense. thanks. Link to comment Share on other sites More sharing options...
timo Posted February 13, 2011 Share Posted February 13, 2011 [math] x^{-1} = \frac {1}{x^{+1}}= \frac 1x [/math] has nothing to do with scientific notation, as far as I know. It's merely a well-known rule for calculations with exponents. Link to comment Share on other sites More sharing options...
1123581321 Posted February 13, 2011 Author Share Posted February 13, 2011 ok, yes sorry, exponents. But what exactly does it mean or imply ? Link to comment Share on other sites More sharing options...
alpha2cen Posted February 13, 2011 Share Posted February 13, 2011 XmXn=X(m+n) For example m=1, n=-2 X1X-2=X(1-2)=X-1 X/X2=1/X Link to comment Share on other sites More sharing options...
Xerxes Posted February 13, 2011 Share Posted February 13, 2011 Would someone be able to please explain to me what the following means - a^-1 = 1/a, a^-m = 1/a^m Well, if you are dealing with a mathematical structure where [math]a^{-1} = \frac{1}{a}[/math] you are implicitly assuming that this structure admits of multiplication and multiplcative identity (here [math]1[/math]). So that [math]1a = a[/math] and [math]aa^{-1} = a \frac{1}{a} = \frac{a}{a} = 1[/math].This is the definition of the multiplicative inverse. But you should be aware that there are structures where [math]a^{-1}a = 0[/math] which implies that [math]a^{-1} = -a[/math]. For these structures the operation in question is called addition, with zero as the additive identity. Maybe you should ignore that point for now, important though it is. So sticking with multiplication, notice that [math]a= a^1[/math] so you simply replace the exponent [math]1[/math] with the exponent [math]m[/math], and it follows that [math]a^{-m} = \frac{1}{a^m}[/math] Link to comment Share on other sites More sharing options...
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