posted by arya .
how am i supposed to use the quotient of powers property to show that zero to the zero power is undefined?
The power of a quotient is equal to the quotient obtained when the dividend and divisor are each raised to the indicated power separately, before the division is performed - so I'm assuming that this is what the quotient of powers property is.
So perhaps the argument would be something like this:
0^0 = 0^(1-1)
= (0^1) / (0^1)
= 0 / 0
which is undefined. (I'm not certain that this is the answer you're looking for, but it seems to fit the question.)