Question

Prove that any number raised to the power of zero will be 1?

Answer 1

This question is quite interesting and Actually has a surprising answer.

The answer is that, we cannot prove that why any number when raised to zero's power is ONE.

Yes!

Although, we may show it like this.

$if \: \: x \not = 0$

$\implies {x}^{0} = {x}^{ n - n }$

For any number n ≠ 0

$\implies {x}^{0} = \frac{ {x}^{n} }{ {x}^{n} } = 1$

But, Actually giving this kind of proof is meaning less. Just because This is not a theorem rather simply a defintion and So can never be proved.

Therefore,

Considering b ≠ 0

${b}^{0} ≝1$

Which implies that the above expression is a definition.

Note that,

IF b would be equal to zero, then We know that

${0}^{0} \: \: i s \: \: \: undefined$

This is similar to if b ≠ 0

${b}^{-1} ≝\frac{1}{b}$

which can never be proved