For this case we have that by definition of power properties:
[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
We have the following expression:
[tex]2 ^ {- 4} * 2 ^ 2 = a ^ b = c[/tex]
It can be rewritten as:
[tex]\frac {2 ^ 2} {2 ^ 4}[/tex]
By definition of power properties we have:
[tex]\frac {a ^ m} {a ^ n} = a ^ {m-n}[/tex]
So:
[tex]\frac {2 ^ 2} {2 ^ 4} = 2 ^ {2-4} = 2 ^ {- 2} = \frac {1} {2 ^ 2} = \frac {1} {4}[/tex]
Thus, [tex]c = \frac {1} {4}[/tex]
Answer:
Option D
