## studyopen101 3 years ago When a number has an exponent of zero, why does it equal 1? Shouldn't it be 0?

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1. kevinkeegan

anything to the power of 0 = 1

2. integralsabiti

anything but 0.

3. integralsabiti

\[0^0\neq0\]

4. kevinkeegan

if all fails use the calculator

5. studyopen101

I know it equals 1, but I want to know why.

6. BMann

no because the rule is 0 exponents always equal 1

7. kevinkeegan

why do you want to know why

8. studyopen101

math teacher told our class to find out

9. m_charron2

I guess you can prove it by stating this : x^y = x^a * x^b (provided that y = a+b) If b = 0, x^b needs to =1, else you'd have x^a * 0 = 0 =/= x^y

10. m_charron2

so by having x^0 = 1, x^a * 1 = x^a = x^(a+0) = x^y. Makes sense?

11. studyopen101

can u plug in numbers to that as an example please?

12. integralsabiti

consider a^1 ÷ a^1 = a / a = 1 but as per laws of indices, a / a = a^(1 – 1) = a^0 = 1 consider a^2 ÷ a^2 = a × a / a × a = 1 but as per laws of indices, a^2 / a^2 = a^(2 – 2) = a^0 = 1 or 5^3 ÷ 5^3 = 125 / 125 = 1 and 5^3 ÷ 5^3 = 5^(3 – 3) = 5^0 = 1 this shows that any number with exponent 0 is equal to 1

13. m_charron2

ah, yes, I much prefer intedralsabiti's proof than mine, a lot simpler

14. m_charron2

his proof also proves that 0^0 doesn't work because you'd need to divide 0 by 0. 0^2/0^2 is impossible, so 0^(2-2) also is, and finally, 0^0 is impossible as well.

15. integralsabiti

i dont deserve that medal.take it back. It is copy-paste

16. m_charron2

bah, then it's a medal for google-searching skills ;-) whatever works really

17. integralsabiti

thx :D