Looks Like Zero to me!

Level 1

W h a t i s 3 0 ? What\quad is\quad { 3 }^{ 0 }?

3 0 1 undefined

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4 solutions

Sravanth C.
Apr 2, 2015

There is actually, I feel, a scientific explanation for why anything to the power of 0 is 0.

Please see the explanation given below,

We know that a m a n = a m n \displaystyle\frac{a^{m}}{a^{n}} = a^{m - n}

Similarly put a = 3 a = 3 and put n = m = 3 n = m = 3

We get 3 3 3 3 = 1 = 3 3 3 = 3 0 \displaystyle\frac{3^{3}}{3^{3}} = 1 = 3^{3-3} = 3^{0}

Hence we can truly say that 3 0 = 1 3^{0} = 1

Thanks for the proof! :)

Maddie Anderson - 6 years, 2 months ago

Yeah! I remember this proof very well... Our maths teacher in 9th class had explained this while teaching the chapter REAL NUMBERS... Do you recall that @Sravanth Chebrolu ??

Skanda Prasad - 6 years, 2 months ago

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I quite well remember it . . .

Sravanth C. - 6 years, 2 months ago
Maddie Anderson
Apr 1, 2015

The exponent 3 0 3^{0} is equal to 1, because we want each value of n for 3 n 3^{n} to be a factor of 3 larger than the preceding value.

For example, 3 0 = 1 3^{0} = 1 , 3 1 = 3 3^{1} = 3 , 3 2 = 9 3^{2} = 9 , and so on. We're basically multiplying the previous value of n by 3.

If 3 0 3^{0} was equal to 0, then 3 1 3^{1} would equal zero as well(because 3 times 0 is zero), and so on until 3 3^{∞} equals zero.

Since we don't want to destroy the very fabric of mathematics itself, we'll stick with 3 0 = 1 3^{0}=1 .

Rama Devi
May 14, 2015

It is very simple because any number to the power zero is equal to 1.

Skanda Prasad
Apr 1, 2015

This is basic,

Anything to the power 0 is 1...

:D :D

Yeah, pretty much. :P My solution also describes why anything to the power of 0 is 1.

(Definitely read it if you want to know why!)

Maddie Anderson - 6 years, 2 months ago

Then what will be 0^0

Suprem s.nalkund - 6 years, 2 months ago

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Hi Suprem, how are you? Enjoying Holidays, I expect... Anyway, Speaking of 0^0... That will also be equal to 1...

Skanda Prasad - 6 years, 2 months ago

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No 0^0 =0

Suprem s.nalkund - 6 years, 2 months ago

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@Suprem S.Nalkund Sorry, but it's 1.

Sravanth C. - 6 years, 2 months ago

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@Sravanth C. But how ???

Suprem s.nalkund - 6 years, 2 months ago

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@Suprem S.Nalkund You can substitute the value zero in place of a a , m m and n n in my explanation above for the answer.

You can also use a calculator to find it!

Sravanth C. - 6 years, 2 months ago

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@Sravanth C. exactly !!

Skanda Prasad - 6 years, 2 months ago

@Suprem S.Nalkund Anyway... Did you solve my new question Think Simply..... 3

Skanda Prasad - 6 years, 2 months ago

@Skanda Prasad , please refer to my solution for a proof . . .

Sravanth C. - 6 years, 2 months ago

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