For this case we have to, by defining properties of powers and roots the following is fulfilled:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
We must rewrite the following expression:
[tex]\sqrt [3] {8 ^ {\frac {1} {4} x}}[/tex]
Applying the property listed we have:
[tex]\sqrt [3] {8 ^ {\frac {1} {4} x}} = 8 ^ {\frac{\frac {1} {4} x} {3} }= 8 ^ {\frac {1} {4 * 3} x} = 8 ^ {\frac {1} {12} x}[/tex]
Using the property again we have to:
[tex]8 ^ {\frac {1} {12} x} = \sqrt [12] {8 ^ x}[/tex]
Thus, the correct option is option C
Answer:
Option C
