hi all

i got some h/w for negative powers teatcher said :

X^-a = 1/X^a

why is that?(Wondering)

thanks.....

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- Sep 8th 2008, 10:48 PMspik31indices laws negative powers
hi all

i got some h/w for negative powers teatcher said :

X^-a = 1/X^a

why is that?(Wondering)

thanks..... - Sep 8th 2008, 11:00 PMo_O
Raising a number to -1 will produce its reciprocal: $\displaystyle {\color{red}x}^{-1} = \frac{1}{{\color{red}x}}$ (this is just how it is defined)

So: $\displaystyle \underbrace{x^{-a} = \left({\color{red}x^{a}}\right)^{-1}}_{\text{Since: } \displaystyle a^{bc} = \left(a^{b}\right)^{c} } \! = \frac{1}{{\color{red}x^{a}}}$ - Sep 8th 2008, 11:27 PMbkarpuz
Because, it is defined to be

$\displaystyle x^{a}x^{b}=x^{a+b},$

letting $\displaystyle b=-a$, we get

$\displaystyle x^{a}x^{-a}=x^{a-a}=x^{0}=1,$

which indicates

$\displaystyle x^{a}=\frac{1}{x^{-a}}\text{ or equivalently }x^{-a}=\frac{1}{x^{a}}$

privided that $\displaystyle x\neq0$. - Sep 9th 2008, 04:07 AMspik31
In english plz ?? (Speechless)(Worried)

That be a great help scince im only startin gcse's :)

thanks all... - Oct 2nd 2008, 10:56 PMCaptainBlack