Answer:
[tex]2^{\frac{1}{4}x}[/tex]
Step-by-step explanation:
[tex]\sqrt[3]{8^{\frac{1}{4}x}}[/tex]
The given radical expression can be written as exponential form
[tex]\sqrt[n]{x} =x^{\frac{1}{n}}[/tex]
we write 8 in exponential form
[tex]8=2*2*2= 2^3[/tex]
we apply the rule to convert it into exponential form
[tex]\sqrt[3]{8^{\frac{1}{4}x}}=\sqrt[3]{2^{\frac{3}{4}x}}=2^{\frac{3}{4}x*\frac{1}{3}}=2^{\frac{1}{4}x}[/tex]
