How do you write 1 as a power in three different ways and why?

Answer 1

For the purposes of this answer we will use the convention that x^n means xⁿ

Any non-zero number to the zero power is 1

we get this from the idea that (x^n)(x^m) is x^(n+m)

if n=-m, then n+m = 0 and x^ m is 1/(x^n) and (x^n)(x^m) (x^n)/(x^n)=1 so x^0 = 1

1 raised to any positive power is 1

1 raised to any negative power is 1

We can thus represent 1 as

x^0 = 1

1^n = 1

1 ^(-n) = 1

(where n>0 Note that n need not be an integer since all roots of 1 are also 1)

Answer 2

Well, honey, you can write 1 as a power in three different ways: 1^1, 1^2, and 1^3. Why? Because any number raised to the power of 1 is just the number itself. So, in this case, 1 raised to the power of 1, 2, or 3 is still just 1. Math can be sassy like that.

Answer 3

1 can be written as (1^1) because any number raised to the power of 1 is equal to the number itself. It can also be written as (1^0) because any number raised to the power of 0 is equal to 1. Additionally, 1 can be written as (e^0), where e is the base of the natural logarithm, because any number raised to the power of 0 is equal to 1.

Answer 4

Oh, dude, writing 1 as a power is like the easiest math question ever. You can write 1 as 1^1, 1^2, or 1^3 because any number to the power of 1 is just that number. It's like saying, "What's 1 to the power of anything?" and the answer is always 1. So, like, yeah, that's why you can write 1 as a power in those three different ways.