1. ## exponent confusion

what is 2^(4-1)^2 ?
(2 raised to (4-1) raised to 2)

2. Originally Posted by vscid
what is 2^(4-1)^2 ?
(2 raised to (4-1) raised to 2)
Hello vscid,

Is this it: $\displaystyle {2^{(4-1)^2}}$ ?

If so, then

$\displaystyle {2^{(4-1)^2}}={2^3}^2=2^9=512$

3. Originally Posted by masters
Hello vscid,

Is this it: $\displaystyle {2^{(4-1)^2}}$ ?

If so, then

$\displaystyle {2^{(4-1)^2}}={2^3}^2=2^9=512$
Why is it not 2^(3*2) = 2^6

4. Originally Posted by vscid
Why is it not 2^(3*2) = 2^6
The way you illustrated the problem, the 3 is taken to the "power of 2" which is 9. It is not 3 * 2. Does my notation match what your original problem says?

5. Originally Posted by masters
The way you illustrated the problem, the 3 is taken to the "power of 2" which is 9. It is not 3 * 2. Does my notation match what your original problem says?
It does.

In which case will it be 2^6 ?

6. $\displaystyle (2^{4-1})^2= (2^3)^2= 8^2= 64$ which is $\displaystyle 2^6$. That is true because $\displaystyle (a^b)^c= a^{bc}$

However, $\displaystyle 2^{(4-1)^2}$ which is how what you wrote should be interpreted, is equal to $\displaystyle 2^{3^2}= 2^9= 512$

7. Originally Posted by HallsofIvy
$\displaystyle (2^{4-1})= (2^3)^2= 8^2= 64$ which is $\displaystyle 2^6$. That is true because $\displaystyle (a^b)^c= a^{b+ c}$

However, $\displaystyle 2^{(4-1)^2}$ which is how what you wrote should be interpreted, is equal to $\displaystyle 2^{3^2}= 2^9= 512$
$\displaystyle (2^{4-1})= (2^3)^2$ ? how come? $\displaystyle 2 to the power (4-1) = 2^3$ and not $\displaystyle (2^3)^2$

8. Originally Posted by vscid
$\displaystyle (2^{4-1})= (2^3)^2$ ? how come? $\displaystyle 2 to the power (4-1) = 2^3$ and not $\displaystyle (2^3)^2$

9. Originally Posted by HallsofIvy
$\displaystyle (2^{4-1})^2= (2^3)^2= 8^2= 64$ which is $\displaystyle 2^6$. That is true because $\displaystyle (a^b)^c= a^{bc}$

However, $\displaystyle 2^{(4-1)^2}$ which is how what you wrote should be interpreted, is equal to $\displaystyle 2^{3^2}= 2^9= 512$
So if there is a bracket, which makes $\displaystyle 2^3$ as the base and 2 as the exponent, then we multiply the powers, however if there is no bracket anywhere, then we do not multiply the powers.

Is that the rule one should follow?

10. Originally Posted by vscid
So if there is a bracket, which makes $\displaystyle 2^3$ as the base and 2 as the exponent, then we multiply the powers, however if there is no bracket anywhere, then we do not multiply the powers.

Is that the rule one should follow?
The rule is when you take a power to a power you multiply the exponents:

$\displaystyle (x^m)^n=x^{mn}$

Yours was a special case. Not only did you want to take the base to a power, you also wanted to take the power to a power.

$\displaystyle {2^3}^2$

In this case you must work from the top down. If you were putting this in a calculator you would have to enter it this way:

2^(3^2) = 512

The parentheses tell the calculator to perform this operation first to get 9, then take 2 to the 9th power to get 512.

If you entered it 2^3^2, you would get 64 because the calculator performs the operations from left to right: 2^3 is 8 and 8^2 is 64.

It's a little tricky when you stack exponents. Just remember to start at the top and work your way down.

Good luck.

11. Originally Posted by masters
The rule is when you take a power to a power you multiply the exponents:

$\displaystyle (x^m)^n=x^{mn}$

Yours was a special case. Not only did you want to take the base to a power, you also wanted to take the power to a power.

$\displaystyle {2^3}^2$

In this case you must work from the top down. If you were putting this in a calculator you would have to enter it this way:

2^(3^2) = 512

The parentheses tell the calculator to perform this operation first to get 9, then take 2 to the 9th power to get 512.

If you entered it 2^3^2, you would get 64 because the calculator performs the operations from left to right: 2^3 is 8 and 8^2 is 64.

It's a little tricky when you stack exponents. Just remember to start at the top and work your way down.

Good luck.
Above you have written: 2^(3^2) = 512.

I do not have the parenthesis in red in my original post. In fact, I should say I have no parenthesis (besides the inevitable (4-1) )

So it is actually 2^3^2.
My question was, if there are no parenthesis as above, then the value will be 2^9 right?