# Imagining something to the power of fraction(1/2,1/3,3/4) on the number line

• February 18th 2013, 04:12 PM
bemineni
Imagining something to the power of fraction(1/2,1/3,3/4) on the number line
Hi,

It took me five minutes to learn latex but finally my question is here.

$x^2 = y$
$x = \sqrt{y}$
$y^\frac{1}{2}=x$

I am able to imagine $x^2$ on the number line in my mind How to imagine something to a power of 1/2 or any fraction on the number line.

Thank you
• February 18th 2013, 04:39 PM
HallsofIvy
Re: Imagining something to the power of fraction(1/2,1/3,3/4) on the number line
You say "finally my question is here", but I see know question!

You say "I am able to imagine on the number line in my mind". What do you mean by that? If x= 2 then $x^2= 4$, a point on the number line, but for general x, $x^2$ can be any point representing a non-negative number.

As for $sqrt{x}= x^{1/2}$, if x= 4 then $\sqrt{x}= 2$ but, for any non-negative x, $\sqrt{x}$ can, again, be any point representing a non-negative number.
• February 18th 2013, 07:36 PM
bemineni
Re: Imagining something to the power of fraction(1/2,1/3,3/4) on the number line
Hi,

$x^3 = x \times x \times x$
$x^\frac{1}{2}$ = ?? represented in the terms of product of x

I know this is basics but please provide the imaginative way to represent this
• February 19th 2013, 09:27 PM
bemineni
Re: Imagining something to the power of fraction(1/2,1/3,3/4) on the number line
$x^3 = x \times x \times x = y$ where y >= x >= 1
$x^\frac{1}{n} = ??? = t$ then 1 <= t <= x and t to the power of the fraction denominator = x
example $\sqrt{2} = 2^\frac{1}{2} = 1.414^2 \approx 2$

I am still not able to get how the reverse of an operation can be represented in the same form

multiplication is the reverse of division. Here I see the reverse of exponentiation can be represented using exponentiation itself but the operation is different and its not exponentiation at all

Exponentiation - Wikipedia, the free encyclopedia.

nth root - Wikipedia, the free encyclopedia

In calculus, roots are treated as special cases of exponentiation, where the exponent is a fraction:

$\sqrt[n]{x} \,=\, x^{1/n}$ = why is this ??