Your answer would be [tex]\sqrt[12]{8}^{2}[/tex].
Approaching this problem would be easier by converting the cube root of 8 to 8 to the power of 1/3. Remember that when you take anything to the nth root, it is the same as taking something to the power of 1 / n.
Therefore, the equation becomes [tex](x^{1/3} )^{\frac{1}{4}x }[/tex].
Now, to keep simplifying, recall that when you do [tex]n^{x^y}[/tex], it can become [tex]n^{x*y}[/tex].
This can be applied in this situation. You are taking 8 to the power of 1/3 to the power of 1/4x. Now, you can multiply the two "to the power of's" to get [tex]8^{\frac{1}{12}x }[/tex]. Applying the same logic, it becomes [tex]8^{\frac{1}{12} *x} = 8^{\frac{1}{12} ^x}[/tex].
Now, all you have to do is use the same logic as used in the very beginning. Raising something to the power of 1/12 can become taking it to the 12th root. So therefore, the equation would be [tex]\sqrt[12]{8}^{x}[/tex]
Good luck!
