To express [tex]\(\sqrt[8]{x^3}\)[/tex] in exponential form, we need to understand the relationship between radicals and exponents.
### Step-by-Step Solution
1. Understanding Radicals and Exponential Form:
- A radical expression like [tex]\(\sqrt[n]{x^m}\)[/tex] can be rewritten in exponential form.
- Specifically, [tex]\(\sqrt[n]{x^m}\)[/tex] is equivalent to [tex]\(x^{\frac{m}{n}}\)[/tex].
2. Application to the Given Expression:
- Here, we have [tex]\(\sqrt[8]{x^3}\)[/tex].
- Following the aforementioned rule, we replace the radical with an exponent: [tex]\(\sqrt[8]{x^3} = x^{\frac{3}{8}}\)[/tex].
### Conclusion
The expression [tex]\(\sqrt[8]{x^3}\)[/tex] is equivalent to [tex]\(x^{\frac{3}{8}}\)[/tex] in exponential form.
Thus, the correct answer is:
[tex]\[ x^{\frac{3}{8}} \][/tex]
