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Power

Power[2, 3]

2 raised to the power of 3 equals 8.

$ wo 'Power[2, 3]'
8

Power[5, 0]

Any number raised to the power of 0 equals 1.

$ wo 'Power[5, 0]'
1

0^0

0 raised to 0 is Indeterminate.

$ wo '0^0'

                                        0
Power::indet: Indeterminate expression 0  encountered.
Indeterminate

$ wo 'Power[0, 0]'

                                        0
Power::indet: Indeterminate expression 0  encountered.
.* (regex*)
Indeterminate

$ wo '0.0^0'

                                         0
Power::indet: Indeterminate expression 0.  encountered.
Indeterminate

Power[2, -1]

2 raised to the power of -1 equals 0.5 (½).

$ wo 'Power[2, -1]'
1/2

Power[4, 0.5]

4 raised to the power of 0.5 equals 2 (square root).

$ wo 'Power[4, 0.5]'
2.

Power[10, 2]

10 raised to the power of 2 equals 100.

$ wo 'Power[10, 2]'
100

Power[-2, 3]

-2 raised to the power of 3 equals -8.

$ wo 'Power[-2, 3]'
-8

Power[-2, 2]

-2 raised to the power of 2 equals 4.

$ wo 'Power[-2, 2]'
4

Power[27, 1/3]

27 raised to the power of ⅓ equals approximately 3 (cube root).

$ wo 'Power[27, 1/3]'
3

Power[1.5, 2.5]

1.5 raised to the power of 2.5 equals approximately 2.756.

$ wo 'Power[1.5, 2.5]'
2.7556759606310752

A base outside the unit circle diverges — to Infinity only when it is a positive real — while one inside it vanishes:

$ wo '{2^Infinity, (-2)^Infinity, (-1/2)^Infinity}'
{Infinity, ComplexInfinity, 0}

Any base on the unit circle never settles:

$ wo '(-1)^Infinity'

                                              Infinity
Infinity::indet: Indeterminate expression (-1)         encountered.
Indeterminate

An infinite base raises its direction, so Sqrt[-Infinity] points along the imaginary axis:

$ wo '{(-Infinity)^(1/2), DirectedInfinity[I]^2, Infinity^Infinity}'
{DirectedInfinity[I], -Infinity, ComplexInfinity}

A negative base with a rational exponent splits its sign off as (-1)^(p/q), and the radical merge folds that sign back into the radicand — so the answer keeps a negative base exactly when nothing can be extracted:

$ wo '{(-2)^(1/3), (-8)^(1/3), (-24)^(1/3), (-12)^(1/3)}'
{(-2)^(1/3), 2*(-1)^(1/3), 2*(-3)^(1/3), (-3)^(1/3)*2^(2/3)}

Half-integer exponents collapse to I:

$ wo '{(-1)^(3/2), (-2)^(3/2), (-4)^(3/2)}'
{-I, (-2*I)*Sqrt[2], -8*I}

Powers of one base add their exponents whatever its sign, while different bases merge under a shared exponent only while their principal values still line up — which allows at most one negative base:

$ wo '{(-1)^(1/3) (-1)^(2/3), 2^(1/3) 2^(1/2), (-1)^(1/3) 2^(1/3), (-2)^(1/3) (-1)^(1/3)}'
{-1, 2^(5/6), (-2)^(1/3), (-2)^(1/3)*(-1)^(1/3)}

^ binds tighter than a leading minus, so -2 ^ 2 is -(2^2) rather than (-2)^2 — spacing around the ^ makes no difference:

$ wo 'Table[-2 ^ n, {n, 2, 4}]'
{-4, -8, -16}

Group explicitly to negate the base:

$ wo '(-2) ^ 2'
4

An integer raised to a negative power is the exact reciprocal, however large the denominator gets:

$ wo 'Head[10^-400]'
Rational

It stays exactly positive even below the range of a machine number:

$ wo '10^-400 > 0'
True