## SWAG 2 years ago Anything raised to the zero power will equal 1. True False

1. SWAG

@jazy

2. SWAG

@jazy ?

3. hba

@SWAG According to exponential rule, $n^0=1$

4. rizwan_uet

its trueeeee

5. TuringTest

what is $0^0$?

6. jazy

But$0^0 = Undefined$

7. SWAG

so that makes it true?

8. rizwan_uet

yes ofcourse

9. asnaseer

@swag - do you know the following rule:$\frac{x^a}{x^b}=x^{a-b}$

10. SWAG

No

11. hba

I think all the mods are in house today :D

12. SWAG

Foreal iv never had so many people or moderators on my question before

13. TuringTest

Technically, most of the time $$0^0$$ is regarded as undefined, but some mathematicians implement the idea that $$0^0=1$$ when the feel that it "makes more sense" so to speak.

14. TuringTest

it's a subtle issue really

15. asnaseer

take a simple case:$\frac{x^4}{x^3}=\frac{x\times x\times x\times x}{x\times x\times x}=x$agreed?

16. cinar

$\Large \infty^0=?$

17. cinar

well, you can say infinity is not a number, but still...

18. SWAG

Right

19. asnaseer

who are you responding to there?

20. SWAG

@asnaseer

21. cinar

it does not a number, it says anything (:

22. hba

Yeah :D

23. TuringTest

I think @asnaseer originally showed me this: http://www.faqs.org/faqs/sci-math-faq/specialnumbers/0to0/#b

24. asnaseer

ok, so you should be able to see now that:$\frac{x^4}{x^3}=x^{4-3}=x^1=x$

25. asnaseer

this is where the rule comes from. so, taking the rule:$\frac{x^a}{x^b}=x^{a-b}$if you let b=a, you get:$\frac{x^a}{x^a}=x^{a-a}=x^0$but:$\frac{x^a}{x^a}=1$therefore:$x^0=1$apart from the case where x=0

26. cinar

$\Large N^0=1$and $\Large 0^N=0$but $\Large 0^0=0$ or $\Large 0^0= 1$?

27. jazy

Anything raised to the zero power will equal 1. <---So this would be False, since not EVERY number follows this rule.

28. hba

No it's debatable

29. asnaseer

if you look at the link @TuringTest posted above, it states under the section "The following is a list of reasons why 0^0 should be 1." some reasons as to why we generally regard $$0^0=1$$

30. jazy

Okay according to my notes in Algebra...it'd be true. I prefer going with what the lesson says. (;

31. TuringTest

here's another good rundown of the trickyness in finding a direct answer http://www.askamathematician.com/2010/12/q-what-does-00-zero-raised-to-the-zeroth-power-equal-why-do-mathematicians-and-high-school-teachers-disagree/

32. hba

I think so that the answer is TRUE.