For this case we have to define root properties:
[tex]\sqrt [n] {a ^ n} = a ^ {\frac {n} {n}} = a[/tex]
In addition, we know that:
[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
On the other hand:
[tex]4 ^ 2 = 16[/tex]
Thus, we can rewrite the given expression as:
[tex]\sqrt {4 ^ 2 * a ^ 8 * \frac {1} {b ^ 2}} =\\4 ^ {\frac {2} {2}} * a ^ {\frac {8} {2}} * \frac {1} {b ^ {\frac {2} {2}}} =\\4 * a ^ 4 * \frac {1} {b}[/tex]
ANswer:
Option B
