A negative exponent means how many times to divide by the number. That last example showed an easier way to handle negative exponents: Calculate the positive exponent (an)
Keeping this in consideration, are positive expressions with negative exponents negative?
Do not apply that here. Remember, you see a negative exponent, that just means the reciprocal of the positive exponent. So 1 over negative 2 to the third power, to the positive third power. And this is equal to 1 over negative 2 times negative 2 times negative 2.
What does a negative and a positive make?
The rule for multiplying and dividing is very similar to the rule for adding and subtracting. When the signs are different the answer is negative. When the signs are the same the answer is positive.
Can we have negative power?
That is, it is flowing in the opposite direction to the direction you defined to be positive. It's just energy flowing the other way, though. As you said, power is just the time rate of change of energy, so it can be negative. But energy is only positive.