For k is an element of the set of natural numbers, and m,n are elements of the set of natural numbers or the set of zero, I have to prove that(adsbygoogle = window.adsbygoogle || []).push({});

1)k^n is an element of the set of natural numbers

2)k^mk^n=k^(m+n)

and

3) (k^m)^n= k^(mn)

I'm pretty confident that these can be shown by induction using the set of whole numbers. But it was never shown in class that k^0=1. Is there any way I can go about showing this? If anyone can just give me some feedback that would be much appreciated as it has been this entire semester. Thanks.

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# Defining things by induction

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