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.

I am able to imagine 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

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 , a point on the number line, but for general x, can be any point representing a non-negative number.

As for , if x= 4 then but, for any non-negative x, can, again, be any point representing a non-negative number.

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

Hi,

= ?? represented in the terms of product of x

I know this is basics but please provide the imaginative way to represent this

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

where y >= x >= 1

then 1 <= t <= x and t to the power of the fraction denominator = x

example

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:

= why is this ??