Can anyone explain me -- Why any number raised to (Power of) zero is always equal to one.
Regards,
Consider Numerical Approach:
$\displaystyle 5^2 = 25$
$\displaystyle 5^1 = 5$
$\displaystyle 5^0= 1$
$\displaystyle 5^{-1}= \frac{1}{5}$
See, We are dividing by 5 each of the power values to get the one below. At any number to the power of zero, we will get one. It's like that for any number.
For example, 9:
$\displaystyle 9^2 = 81$
$\displaystyle 9^1 = 9$
$\displaystyle 9^0= 1$
$\displaystyle 9^{-1}= \frac{1}{9}$
Well that is not always true $\displaystyle 0^0$ is not defined.
However, if $\displaystyle x \ne 0 \Rightarrow \quad x^0 = 1$.
Every nonzero number has a multiplicative inverse denoted by $\displaystyle x^{-1}$.
Use the law of exponents: $\displaystyle 1 = \left( x \right)\left( {x^{ - 1} } \right) = x^{1 - 1} = x^0 $
Alternatively: $\displaystyle 1 = \frac{{x^k }}{{x^k }} = x^{k - k} = x^0 $