why is 2^8, 256 and not 512?

[Icyculyr Fr0st]

Just wondering why 2^8 = 256 and not 512?

can anyone explain that to me lol?

[tommygrayson]

Just wondering why 2^8 = 256 and not 512?

can anyone explain that to me lol?

2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
2^7 = 128
2^8 = 256

Hope that helps.

[Icyculyr Fr0st]

2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
2^7 = 128
2^8 = 256

Thanks, but I knew that, but im wondering why

2^1 = 2, shouldn't 2^1 = 4? ((2*2)*1) = 4?
just wondering why its 2 and not 4 lol

[vb2dub]

2x2x2x2x2x2x2x2 = 2^8 = 256
2 = hmm.... = 2^1 = 2
2x2 = 4 = 2^2 = 4

etc..

[Icyculyr Fr0st]

ok, that makes sense, thanks

[tommygrayson]

Thanks, but I knew that, but im wondering why

2^1 = 2, shouldn't 2^1 = 4? ((2*2)*1) = 4?
just wondering why its 2 and not 4 lol

Just think that ^n is the number of times you have to multiply the same number.

For example:

2^0 = 0

Because ^0 is 0 times to multiply 2. In other words.

2*0 = 0

2^1 = 2

Because ^1 is 1 time to multiply 2. In other words.

2*1 = 2

2^2 = 4

Because ^2 is 2 times to multiply 2. In other words.

2*2 = 4

2^3 = 8

Because ^3 is 3 times to multiply 2. In other words.

2*2*2

And so on and so forth.

[penagate]

n⁰ is 1, not 0.

[tommygrayson]

n⁰ is 1, not 0.

Oh yeah.

Sorry about that.

[penagate]

Easy way to visualise it:

n⁰ = 1
n¹ = n
n² = nn
n³ = nnn
n⁴ = nnnn
n^k = nnnnn...[k]

[dsheller]

Easy way to visualise it:

n⁰ = 1
n¹ = n
n² = nn
n³ = nnn
n⁴ = nnnn
n^k = nnnnn...[k]

And by the nn he means n*n, just in case someone ever reads this thread and is confused.

[NickThissen]

Easy way to visualise it:

n⁰ = 1
n¹ = n
n² = nn
n³ = nnn
n⁴ = nnnn
n^k = nnnnn...[k]

Just to add to this:

n^-1 = 1 / n
n^-2 = 1 / (nn)
n^-3 = 1 / (nnn)
n^-x = 1 / (nnnnn ... [x])

[RhinoBull]

For example:

2^0 = 0

Because ^0 is 0 times to multiply 2. In other words.

As pointed by penagate any number (other than zero of course) raised to the power zero has a numerical value of 1 - that is absolutely correct and here is why:

power can be

POSITIVE:
3 ^ 2 = 9

NEGATIVE:
3 ^ -2 = 1/9

ZERO:
3 ^ (2-2) = 9/9 = 1

[Lord Orwell]

its also easily visualized with powers of 10 and decimal points.
10^-1 = .10
10^+0 = 1.0
10^+1 = 10.0

It works exactly the same way no matter what base. You just move your decimal.