Exponent Tower

This problem has the potential to confuse many. Just for those who got trapped, don't get confuse between $2^{3^{2}}$ and $(2^{3})^{2}$ . The latter one opens to $2^{3 \times 2}$ , which has a completely different meaning.

What we want is $2^{3^{2}}$ , which is actually $2$ to the power $3$ to the power $2$ . Hence we would simplify it as-

$2^{3^{2}}$ $= 2^{9}$ $= \fbox{512}$ .

Hence the required value is $\fbox{512}$ .

Don't think of $2^{3^2}$ as $(2^3)^2 = 2^6$

Instead it is $2^{(3^2)}$

So, firstly evaluate $3^2$ which is $9$

Now finally evaluate $2^9$ which comes to 512

From The question , we simplify $2^{3^{2}}$ to $2^{9}$ = $\boxed{512}$

easy ya ? forget the calculator now :D

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

Laws of exponents are applied here. first of all we will take the square of the exponent(3) of 2. the exponent of 2 will become 9 which is equal to 512

2^n^m = 512 where: n=3 m=2

n^m = 3^2 = 9 2^9 = 512

2^3^2=2^9=512

2^(3^2)=2^9=512

first find 3 power 2 which is nothing but 9 then calculate 2 power 9 which leads to the answer

2^3^2= 2^9

2^9= 512

I put 2 to the third power then i squared it and it gave me 512

2^9=512..

3E2=9.then use 9 as the exponent of 2. 2E9=512

I pulled 2^3^2 in the calculator and got 512.

2^(3^2)= 2^9= 512

what you do is pretend that the the base two is not there and you square the the 3 by 2 then turns out to be 9 then you use the result as the exponent and do 2 to the ninth power

2 and power 3 & 2 first (3 3)=9 then power of 2 is 9 then multiply 2 nine time with 2 2 2 2 2 2 2 2 2*2= 512

(2)^(3^2)= $2^{9}$

$2^{9}$ = 2 x 2 x 2... x 2 = 512

$2^{3^2}=2^{(3^2)}=2^9=\boxed{512}$

$3^2=9$ , and $2^9=\boxed{512}$ , which is our answer.