1. The problem asks to find the value of 8 raised to the power of $\frac{1}{3}$ using rational exponents. 2. The formula for rational exponents is $a^{\frac{m}{n}} = \sqrt[n]{a^m}$, where $a$ is the base, $m$ is the numerator, and $n$ is the denominator of the exponent. 3. In this case, $8^{\frac{1}{3}}$ means the cube root of 8, or $\sqrt[3]{8}$. 4. We know that $8 = 2^3$, so substituting this gives $\sqrt[3]{2^3}$. 5. Using the property of roots and exponents, $\sqrt[3]{2^3} = 2^{\cancel{3}/3} = 2^1$. 6. Simplifying, $2^1 = 2$. 7. Therefore, the solution to $8^{\frac{1}{3}}$ is 2.