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Why is raising a number to the power of 1/2 the same as finding the square root of the number?

Can someone please help. Please provide examples. I would appreciate it if you guys can help as soon as possible.

  • Math -

    Patience, child. I've deleted 3 of these duplicate posts in the last few minutes. Do not post this question again for at least 3 hours.

  • Math -

    Sorry, I didn't know that you delete duplicate posts. I have only just started using this site a couple days ago.

  • Math -

    We know that
    (√x)^2 = x , by the very definition of √x

    suppose we take x(1/2) and square it
    by the exponents rules this would be
    x( (1/2)(2) )
    = x
    so (√x)^2 = (x^(1/2) )^2
    then √x = x^(1/2)

    so x^(1/2) behaves the same way as √x

    by the same argument we can show that
    x^(1/3) is the same as ∛x
    x^(1/4) is the same as ∜x

  • Math -

    Thank you. I appreciate it.

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