Im a bit confused with this concept. (2^2)^4= 2^8 but

2^2^2^2

=2^2^4

= 2^16

In the first case we are just multiplying the exponents 2 by 4 and in the second case we are taking the root of the exponents? why is that?

Im a bit confused with this concept. (2^2)^4= 2^8 but

2^2^2^2

=2^2^4

= 2^16

In the first case we are just multiplying the exponents 2 by 4 and in the second case we are taking the root of the exponents? why is that?

Look at this from left to right.

Sorry I don’t get it

2^2^2^2

Start from left to right. 2^2 = 4. Then you have

4^2^2

4^2 = 16. Then you have

16^2 = 256 (this is the same as 2^{8}).

So when do we multiple exponents with each other and when do we take the power and continue taking the power?

Normally left to right unless brackets make it clear how you take the exponents.