Inifinity questions?

Question

What do these equal? They are either indeterminate, Non-existant or a number
a) 1^-infinity
b)infinity^-e
c) 0^-infinity
d) 1/(-infinity)
e)pi^infinity
f)infinity^-infinity
g)pi^-infinity
h)(infinity).(infinity)
i)infinity^infinity

If you could give a quick explanation it would be helpful. THanks!

Answer 1

Wow, people need to start learning that infinity is NOT a real number.

Answer 2

Infinity isn't a number, so I'm going to pretend that you asked questions like

(a) limit (x -> infinity) 1 ^ -x

and so on.

(a) 1 raised to any power, positive or negative, is 1
(b) x ^ -e = 1 / x ^ e becomes zero when x goes to infinity
(c) 0 raised to any power is...well, see the link.
(d) 1 / -x becomes zero as x goes to infinity
(e) pi ^ x becomes infinite as x goes to infinity
(f) x ^ -x = 1 / x^x becomes zero as x goes to infinity
(g) pi ^ -x = 1 / pi ^ x goes to zero as x goes to infinity
(h) x^2 becomes infinite as x goes to infinity
(i) x^x becomes infinite as x goes to infinity

Answer 3

Do keep in mind that infinity is a concept, so these answers are not necessarily debatable, but can be considered "wrong".

a) 1^-infinity = 1
b) infinity^-e = 1/"big" -> 0
c) 0^infinity: undefine
d) -1/infinity -> 0
e) pi^infinity -> infinity
f) infinity^-infinity = 1/"BIG" -> 0
g) pi^-infinity = 1/"big" -> 0
h) infinity.infinity: ???
i) infinity^infinity = big^big -> infinity