Why is a number to the first power equal the same number?

Answer 1

The following is not a proof or a reason, but it's a demonstration

that might be intuitively satisfying:

'X' mentioned 4 times: X times X times X times X = X to the fourth power

'X' mentioned 3 times: X times X times X = X to the third power

'X' mentioned 2 times: X times X = X to the second power

'X' mentioned 1 time: X = X to the first power

But this is not the question you should be asking. What you should really be

worrying about is:

"Why is a number to the zero power equal 1 ?" Answer:Let's use 3 as an example:

33=27

32=9

31=3 <--- The one you asked about

30=1

Spreading this out so we can see what's going on:

33= 1x3x3x3=27 (one times three, three times)

32=1x3x3=9

31=1x3=3 <--- The one you asked about

30=1x(no number)=1

So a number raised to a power is one times that number the same number of times as the power.

For a number raised to the first power it is one times that number once, which equals the number itself.