# Double Exponents

• Mar 14th 2013, 04:25 PM
dnftp
Double Exponents
I want to find 2^3^(k+1) in terms of k.
I think that 2^3^(k+1)=(2^3^k)^3 is true, however I don't understand how to manipulate these double exponents
I have looked for 'rules' unsuccessfully, can anyone enlighten me?
Also if someone could please show me how to write double exponents in latex that would be great.
• Mar 14th 2013, 05:00 PM
Soroban
Re: Double Exponents
Hello, dnftp!

I have two issues with this problem . . .

Quote:

I want to find 2^3^(k+1) in terms of k.

[1] The expression is already in terms of $\displaystyle k.$
. . .So what are they asking us to do?

[2] There are two ways to read this problem.

. . .$\displaystyle \displaystyle(2^3)^{k+1}\:\text{ and }\;2^{3^{k+1}}$
• Mar 14th 2013, 05:52 PM
dnftp
Re: Double Exponents
Hi, Soroban
Yes I worded the question badly.
I want to use induction to prove a statement.
I have been given $\displaystyle 2^{3^{k}}$, I apply the inductive step k + 1, to get $\displaystyle 2^{3^{k+1}}$, and want to rewrite this without k+1, just k.
What I had previously written was $\displaystyle 2^{3^{k+1}} = (2^{3^{k}})^3$
• Mar 14th 2013, 08:38 PM
ibdutt
Re: Double Exponents
There is some confusion in writing the question. I do not find a statement that you want to prove by Mathematical Induction. Please recheck and post it again.
• Mar 14th 2013, 09:46 PM
dnftp
Re: Double Exponents
I don't need help with the induction, I was trying to give an indication of why I was asking.