Clarifying Mathematical Confusion: The Truth About 1010101010

[Nick666]

My math is rusty so please tell me

10^10101010[/size] does not equal (((10¹⁰)¹⁰)¹⁰)¹⁰ , right ?

 

[Mark44]

Right. You have to work your way down rather than work you way up the chain of exponents.

Here's a simpler example:
$$10^{2^3}$$

If you worked your way up through the exponents, this would be (10²)³ = 10⁶
If you work your way down, you get 10⁽²³⁾ = 10⁸

 

[Nick666]

Allright, so here we go

=10^1010100[/size]

=10^{101followed by 100 zeros}[/size]

=10^{1followed by 10000 trillion trillion trillion trillion trillion trillion trillion trillion of zeros} [/size][/color]

=...

My question is, and maybe this should be moved on another forum,

Can the number be calculated ? I mean the observable universe has like "1followed by ~80 zeros" atoms , so a number like the one above can't be calculated right ? I can't imagine a machinery in this universe even operating with the number written in red... What about a quantum computer ?

 

[HallsofIvy]

What do you mean by "calculated"? I honestly don't see how the number of atoms in the observable universe has anything to do with calculating a number.