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Math Help - any no raised to zero

  1. #1
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    Question any no raised to zero

    Can anyone explain me -- Why any number raised to (Power of) zero is always equal to one.

    Regards,
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  2. #2
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    Consider Numerical Approach:

    5^2 = 25
    5^1 = 5
    5^0= 1
    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:
    9^2 = 81
    9^1 = 9
    9^0= 1
    9^{-1}= \frac{1}{9}
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by avinash View Post
    Can anyone explain me -- Why any number raised to (Power of) zero is always equal to one.

    Regards,
    Well 0^0 is undefined, but other than that it is so that a^xa^y=a^{x+y} works for any real x and y and a >0 . Also for other consistency reasons.

    RonL
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  4. #4
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    Quote Originally Posted by avinash View Post
    Can anyone explain me -- Why any number raised to (Power of) zero is always equal to one.

    Well that is not always true 0^0 is not defined
    .
    However, if x \ne 0 \Rightarrow \quad x^0  = 1.
    Every nonzero number has a multiplicative inverse denoted by x^{-1}.
    Use the law of exponents: 1 = \left( x \right)\left( {x^{ - 1} } \right) = x^{1 - 1}  = x^0

    Alternatively: 1 = \frac{{x^k }}{{x^k }} = x^{k - k}  = x^0
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