1. ## Negative fractional indices

Rewrite x^(-3/2) without negative indices.

I thought it would be x^(2/3)... why is this not correct?

Also what is the difference between indices and exponents?

2. Originally Posted by olivia59
Rewrite x^(-3/2) without negative indices.

I thought it would be x^(2/3)... why is this not correct?

Also what is the difference between indices and exponents?
recall, $\displaystyle x^{-a} = \frac 1{x^a}$ where $\displaystyle x \ne 0$

now try again

indices are exponents. just different names for the same thing. they are also called powers. ("indices" may refer to other things also, but here it means exponents)

3. Originally Posted by Jhevon
recall, $\displaystyle x^{-a} = \frac 1{x^a}$ where $\displaystyle x \ne 0$

now try again

indices are exponents. just different names for the same thing. they are also called powers. ("indices" may refer to other things also, but here it means exponents)
But I thought a 1/x was the same as the inverse. And inverse is the recipricol? And the recipricol of -3/2 is 2/3 is it not?

4. so would you say that $\displaystyle \frac{-3}{2}=\frac{2}{3}$?

I think you are getting confused with what is meant by 'it becomes the inverse'. When the power is negative, it means that the 'x' (in this case) is the reciprocal.

I've explained it very badly, so here are some examples.

$\displaystyle x^{-4}=\frac{1}{x^4}$

$\displaystyle 3^{-2}=\frac{1}{3^2}$

$\displaystyle 2x^{-5}=\frac{2}{x^5}$

It's probably easier to ignore the negative part to start with, and work out what it would look like just as a fractional power. Then take the reciprocal.

Eg:

$\displaystyle x^{\displaystyle\frac{-5}{2}}$

So look at:

$\displaystyle x^{\displaystyle\frac{5}{2}}$

$\displaystyle =\sqrt{x^5}$

Therefore:
$\displaystyle x^{\displaystyle\frac{-5}{2}}$
$\displaystyle =\frac{1}{\sqrt{x^5}}$