If you have -3 with a -4 exponent
If you have -3 with a -4 exponent
Negative exponents have the following property: n^{-m }= 1/n^{m} OR 1/n^{-m} = n^{m}
So for (-3)^{-4} , n= -3 and -m= -4 (or m= 4).
Thus, (-3)^{-4} = 1/(-3)^{4}.
We can rewrite (-3^{-4}) using a positive exponent by taking the reciprocal of the base (-3) and applying the absolute value of the negative exponent (-4) to the denominator of the fraction like this: 1/(-3)^{4}. Now we can simplify the denominator by evaluating (-3)^{4} which is the same as writing (-3)(-3)(-3)(-3) giving us 81. So our fraction in simplest form is 1/81. One interesting thing to note here is that raising a negative number by an even numbered exponent gives a positive value (as in our case) and raising a negative number by an odd numbered exponent yields a negative result.