By definition, $x^1$=$x$ and $\sqrt[1]{x}$ = $x$
My own personal understanding of this rule is just rote memory, so if you were to ask me to explain why I wouldn't know what to say. For example does $9^1 = 9\cdot1$ ? Intuitively I would say yes because it gets the desired result, but somehow I doubt that's what it means.
Never mind the second definition with the first root. Absolutely no idea how that works (besides memorizing it for calculations of course).
Any explanation/proof appreciated. Thanks.
I think both are true by definition, since $\sqrt[1]{x}=x^{\dfrac{1}{1}}=x^{1}$ and: (from Wikipedia)