Answer:
Option A is correct.
\(-4^{-4}\)
Step-by-step explanation:
Using exponent rule:
\((a^{-n})^m =(\frac{1}{a^n})^m = \frac{1}{a^{nm}}\)
Option A:
\(-4^{-4}\)
\(-(4^{-1})^4 = -(\frac{1}{4})^4 = -\frac{1}{4^4} = -\frac{1}{256}\)
Option B:
\((-4)^{-4}\)
\((-4)^{-4} = ((-4)^{-1})^{4} = (\frac{1}{-4})^4 = \frac{1}{(-4)^4} = \frac{1}{256}\)
Option C :
\(4^{-4}\)
\(4^{-4} = (4^{-1})^4 = (\frac{1}{4})^4 = \frac{1}{4^4} = \frac{1}{256}\)
Option D:
\((\frac{1}{4})^{-4}\)
\((\frac{1}{4})^{-4} = (4^{-1})^{-4}=4^{4} = 256\)
Therefore, the following simplifies to a negative number is, \(-4^{-4}\)
