Answer:
Given : [tex](\sqrt[3]{8})^{\frac{1}{4}x}[/tex]
Use exponent rules:
[tex]\sqrt[n]{a^m} = (a^m)^{\frac{1}{n} }= a^{\frac{m}{n}}[/tex]
then;
[tex](8^{\frac{1}{3}} )^{\frac{1}{4}x}[/tex]
[tex](8)^{\frac{1}{3 \cdot 4}x}[/tex]
[tex]8^{\frac{1}{12}x}[/tex]
or
[tex](\sqrt[12]{8})^{x}[/tex]
Therefore, the expression which is equivalent to [tex](\sqrt[3]{8})^{\frac{1}{4}x}[/tex] is, [tex](\sqrt[12]{8})^{x}[/tex]
