simple question...i think: wouldn't 10^10^123 be the same as 10^124?

[ifantis]

Ok so the tv was on in the background and they were talking about string theory and the amount of information in the universe, and they used the equation 10^10^123 to show how much information was in the universe. I know its a really absurd number, but my question is this, having completed nothing above algebra i know that 10^10 is 10 with 10 zeros on it, so wouldn't 10^10^123 be the same as 10^124? if so why call it ten to the tenth to the 123rd power? why wouldn't they just say 10 to the 124th power? Sorry if this is a dumb question I just like to soak up knowledge and its not very often I don't understand something but this one has me a little confused

 

[ksdhart2]

When applying the carat operator, the typical method is to go left-to-right, such that 10^10^123 becomes 10¹⁰¹²³ or, if written out, a 1 followed by 10¹²³ zeros. That's a staggeringly large number, certainly FAR bigger than 10¹²⁴. Further, even if there were parentheses involved to tell us to do operations in a different order: (10^10)^123 = 10000000000¹²³ = 10¹²³⁰, which is still much bigger than 10¹²⁴, though not nearly as large as the first number. What you might be thinking of is 10 times 10^123. 10*(10¹²³) = 10¹ * 10¹²³ = 10¹²⁴.