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+0

# 0 to the power of 0

0
352
4
+74

Should 0be 0 or 1?

This has always been a strong frustration source for me.

May 8, 2018

### 3+0 Answers

#1
+985
+2

hi beary!

if you ask the calculator, it says it is zero.

however, the alternating sum of binomial coefficients from the n-th row of Pascal's triangle is what you obtain by expanding (1-1)^n using the binomial theorem, i.e., 0n.

But the alternating sum of the entries of every row except the top row is 0, since 0^k=0 for all k greater than 1.

But the top row of Pascal's triangle contains a single 1, so its alternating sum is 1, which supports the notion that (1-1)^0=0^0 if it were defined, should be 1.

so therefore 0^0 is zero.

i hope this helped,

gavin

May 8, 2018
#2
+101322
+3

00  is an indeterminant form...here's why ...

Note...if we let n be any real number...we have

00  =  0 n-n  =  0n  / 0  =    0  / 0

But also note that    0  / 0   =  pi        or  0 / 0    =  11   or   0 / 0  = e  ......  etc....

Thus....we  can't actually determine  the value  of  0n-n  = 0

May 8, 2018
#3
+1354
+1

Its zero

May 8, 2018