# Math Help - Exponent Exponents?

1. ## Exponent Exponents?

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

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

Example:

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

That's different from:

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

Does that help?

3. That is great, thanks.

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

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

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 $3^{2^{3^2}}$

$3^{2^9}$

$3^{512}$

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