Answer:
![(\sqrt[3]{x} )^8](https://img.qammunity.org/2022/formulas/mathematics/high-school/f8k9wf19zhorwvyqk1pxw9vyisdroymjtb.png)
Explanation:
Radical expression :
Cube root of any expression 'a' =
![\sqrt[3]{a}](https://img.qammunity.org/2022/formulas/mathematics/college/tx4guo8uh99d7lgxfz65cljd90e3q4uad3.png)
Radical exponent:
'a' to the power n =

Similarly cube root of x =
![\sqrt[3]{x}](https://img.qammunity.org/2022/formulas/mathematics/high-school/ljpr8r7acnwd2q02ae2aczfwxaocn53jha.png)
cube root of x to the power of 8 =
![(\sqrt[3]{x} )^8](https://img.qammunity.org/2022/formulas/mathematics/high-school/f8k9wf19zhorwvyqk1pxw9vyisdroymjtb.png)
Now , the required radical expression with rational exponents for "cube root of x to the power of 8" =
![(\sqrt[3]{x} )^8](https://img.qammunity.org/2022/formulas/mathematics/high-school/f8k9wf19zhorwvyqk1pxw9vyisdroymjtb.png)
Hence, the required expression =
![(\sqrt[3]{x} )^8](https://img.qammunity.org/2022/formulas/mathematics/high-school/f8k9wf19zhorwvyqk1pxw9vyisdroymjtb.png)