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