Why 4^0 = 1?

Question

I don't get it. If there is nothing, how can it be one?

Answer 1

Well:

(4^x)/(4^y) = 4^(x-y) as you mayhave learned (and is shown in the answer above)

So:

(4^x) / (4^x) = 4 ^ (x-x) = 4 ^ 0, but
(4^x)/(4^x) = 1, obviously, so
4 ^ 0 = 1

This counts for 0 as well. 0 ^ 0 = 1

Answer 2

As the exponent increases by +1, the value increases by X4

Starting arbitrarily at 4^-5, notice the sequence

1/1024=4^-5
1/256=4^-4
1/64=4^-3
1/16=4^-2
1/4=4^-1

1=4^0

4=4^1
16=4^2
64=4^3
256=4^4
1024=4^5
......

It's the same for any number, not just 4
X^0=1, for all numbers

Answer 3

4^2 = 16
4^1 = 4

16/4 = 4

4^1 = 4
4^0 = 1

4/1 = 4

Got it?

Each decrement in the exponent is just like division by 4!

(Furthermore: 4^(-1) = 1/4, 4^(-2) = 1/16. Just keep dividing by 4)


Exponentiation should be thought of as "the number of times 1 is multiplied by the base" NOT "how many times the base is multiplied by itself"

Answer 4

4^0=4^(x-x)=4^x/4^x(by law of indices)=1

Answer 5

4^4/4^4 = 1

4^4/4^4 = 4^(4-4)

4^(4-4) = 4^0

Therefore, 4^0 = 1

Answer 6

If you want to know why anything raised to the 0 power is 1, the reason is that this is a mathematical definition for something that doesn't really exist, but when this is done all other equations work out.

Answer 7

x^a divided by x^a=x^(a-a)=x^0 ( in ddvn. poers r subtracted.) AgainX^a divided byX^a=1 (denominator=numerator) Hence X^=1.