On algebraic operations involving $-\infty$ and $+\infty$

Question

$-\infty$ and $+\infty$ are two mathematical objects that we attach to the real number system to extend it. These objects are governed by a set of properties. However, I'm confused on a few points. Any clarification on these points would be greatly appreciated.

$(i)$ Are $\frac{1}{\infty}$ and $\frac{1}{-\infty}$ indeterminate$?$ Or they are equal to $0?$

$(ii)$ Is $\left(+\infty\right)^{\left(+\infty\right)}$ indeterminate or $+\infty?$

$(iii)$ For $-\infty<x<0,$ $\left(+\infty\right)^x=?$

$(iv)$ $\left(+\infty\right)^{\left(-\infty\right)}=?$

$(v)$ $0^{\left(+\infty\right)}=?$

$(vi)$ For $-\infty<x<0,$ $x^{\left(+\infty\right)}=?$

$(vii)$ $\left(-\infty\right)^{\left(+\infty\right)}=?$

Thanks in advance!

Answer 1

1. They are equal to $0$.
2. It is $+\infty$.
3. $0$.
4. $0$.
5. $0$.
6. It's indeterminate.
7. It has no meaning.