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How do I use the quotient of powers property to show that zero to the zero power is undefined?

  • math -

    Think of x^n = (x^(n+1)) / x

    so if x^1 =x, then x^0 = (x^1) / x = x / x =1

    If x = 0 then: 0^1 = 0, so x ^ 0 = 0 / 0

    now x / n heads towards (positive or negative) infinity as n becomes closer to 0.
    As infinity is not a number, x / 0 has no numeric solution.

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