Indices-classical analysis

Laws of Indices

Im looking for a proof for the following three terms which have the name
'Laws of Indices' assigned to them.

Let m,n be elements of N. Let a be greater than or equal to zero. Then

1) a^1/m.a^1/n= a^1/mn
2) (a^m)^1/n = (a^1/n)^m

3) If b >= 0 then
(ab)^1/n = (a^1/n)(b^1/n)


From the viewpoint of analysis,
you would begin by proving
a^(m/n) stands for (a^1/n)^m
and the three laws come from it.

Any ideas how this statement and the three laws derived from it would be
proved?



.

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