Yes. -2^3, for example, is -8.
This question is ambiguous - the questioner may mean "can the exponent be negative".
In which case 2-3 is 1/8 or 0.125.
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Please consider the following two facts: A negative number to an even power is positive; but a negative number to an odd power is negative. Any positive number is greater than any negative number.
When a negative number is raised to an even power the result is a positive number
A negative power. When something is to the power of negative two, say X it would be 1/X. If something is to the power of negative 3, it would be.... etc
The result will be a negative value.
It does not work that way. A negative power is simply the reciprocal. So that x-a = 1/xa The reciprocal is negative or positive according to whether the number itself is negative or positive. [And, if the number is 0, the reciprocal is not defined.]