indices laws negative powers

**spik31** · September 8th 2008, 10:48 PM

hi all
i got some h/w for negative powers teatcher said :
X^-a = 1/X^a
why is that?

thanks.....

**o_O** · September 8th 2008, 11:00 PM

Raising a number to -1 will produce its reciprocal: ${\color{red}x}^{-1} = \frac{1}{{\color{red}x}}$ (this is just how it is defined)

So: $\underbrace{x^{-a} = \left({\color{red}x^{a}}\right)^{-1}}_{\text{Since: } \displaystyle a^{bc} = \left(a^{b}\right)^{c} } \! = \frac{1}{{\color{red}x^{a}}}$

**bkarpuz** · September 8th 2008, 11:27 PM

Because, it is defined to be
$x^{a}x^{b}=x^{a+b},$
letting $b=-a$ , we get
$x^{a}x^{-a}=x^{a-a}=x^{0}=1,$
which indicates
$x^{a}=\frac{1}{x^{-a}}\text{ or equivalently }x^{-a}=\frac{1}{x^{a}}$
privided that $x\neq0$ .

**spik31** · September 9th 2008, 04:07 AM

In english plz ??

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

thanks all...

**CaptainBlack** · October 2nd 2008, 10:56 PM

Originally Posted by spik31

In english plz ??

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

thanks all...

I think this is a d**n cheek, try posting in English yourself.

RonL

Thread: indices laws negative powers

LinkBack

Thread Tools

Display

indices laws negative powers

Similar Math Help Forum Discussions

Negative indices

Exponent Equations (Laws of Indices)

negative indices

Negative Indices

Powers/Indices

Search Tags