Is 0 to the power of 0 equals 0 a final answer?

Answer 1

Yes, 0 to the power of 0 equals 0 is a final answer.

1. The law of exponentiation

All of the nth exponentiation of the same base a

has the same: a base constants.

All of the exponentiation of any base a with the same exponent n has the same: n+1 exponent constants.

All of the exponentiation an is analized and arranged unique by order and is equal to sums of meaning productsof:

every base constant (from number 1, among abase constants, to the last number 1),

with

every exponent constant (from number 1, among n+1 exponent constants, to the last number n!).

2. The formula of exponentiation law

an =1×1 + (a-1)(2n-1) +…+ (a-1)×0,5[(n+1)!] + 1×n!

3. 10000, 100, 20, 10, 00...?

10000 According to the law:

a=1000 has 1000 base constants (1, 999, ..., 999, 1),

n=0 has 1 exponent constant (1), from there:

10000=1×1+999×0=1+0=1

· 100 According to the law:

a=10 has 10 base constants (1, 9, ..., 9, 1),

n=0 has 1 exponent constant (1), from there:

100=1×1+9×0=1+0=1

· 20 According to the law:

a=2 has 2 base constants (1, 1), n=0 has 1 exponent constant (1), from there:

20=1×1+1×0=1+0=1

· 10 According to the law:

a=1 has 1 base constant (1), n=1 has 1 exponent constant (1) from there:

10=1×1+0×0=1+0=1

· 00 According to the law:

a=0 has 0 base constant (0), n=0 has 1 exponent constant (1), from there:

00=0×1=0

00 = 0×1 = 0 is a final answer.

00 = 1 is not a final answer.

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