0**x goes undefined when x falls below 1

Eh? The squareroot of 0 is still 0, AFAIK. And that's where the value of the exponent is 1/2: SQRT(0) == 0**0.5. I see no reason for a change in behaviour when x gets closer to 0.

Perhaps you ment to say "when x falls below 0"? Because 0**x is 0 for any x > 0, and 0**x is infinite for any x < 0.