1. The problem asks to find the value of $8^{\frac{1}{3}}$. 2. The expression $a^{\frac{m}{n}}$ means the $n$th root of $a$ raised to the $m$th power, or equivalently, $\left(\sqrt[n]{a}\right)^m$. 3. Here, $8^{\frac{1}{3}}$ means the cube root of 8, since the numerator is 1 and the denominator is 3. 4. We know that $8 = 2^3$, so the cube root of 8 is the cube root of $2^3$. 5. Using the property of exponents, $\sqrt[3]{2^3} = 2^{\frac{3}{3}} = 2^1 = 2$. 6. Therefore, $8^{\frac{1}{3}} = 2$. Final answer: $2$