1. ## Exponent Exponents?

Please could somebody explain to me what $\displaystyle x^{y^z}$ equals. I know that when the second power is in brackets the powers multiply, e.g. $\displaystyle (x^y)^z$ = $\displaystyle x^{yz}$ but I do not know what to do when the indices are not separated by brackets.

2. Originally Posted by Bruce
Please could somebody explain to me what $\displaystyle x^{y^z}$ equals. I know that when the second power is in brackets the powers multiply, e.g. $\displaystyle (x^y)^z$ = $\displaystyle x^{yz}$ but I do not know what to do when the indices are not separated by brackets.
Hi Bruce,

$\displaystyle x^{y^z}$ means you find $\displaystyle y^z$ first, then you raise x to that exponent value.

Example:

$\displaystyle 2^{3^2}=2^9=512$

That's different from:

$\displaystyle (2^3)^2=8^2=64$

Does that help?

3. That is great, thanks.

To check my understanding, is $\displaystyle 3^{2^{3^2}}$

$\displaystyle 3^{2^9}$
$\displaystyle 3^{512}$

So you work down finding each single power first from the top.

4. Originally Posted by Bruce
That is great, thanks.

To check my understanding, is $\displaystyle 3^{2^{3^2}}$

$\displaystyle 3^{2^9}$

$\displaystyle 3^{512}$

So you work down finding each single power first from the top.
Yes, Bruce. That is correct. BTW, that's a huge number.