1. The problem is to find the value of $8^{\frac{1}{3}}$. 2. The expression $a^{\frac{1}{n}}$ means the $n$th root of $a$. So, $8^{\frac{1}{3}}$ means the cube root of 8. 3. The cube root of a number $x$ is a number $y$ such that $y^3 = x$. 4. We want to find $y$ such that $y^3 = 8$. 5. Since $2^3 = 2 \times 2 \times 2 = 8$, it follows that $y = 2$. 6. Therefore, $8^{\frac{1}{3}} = 2$. Final answer: $$8^{\frac{1}{3}} = 2$$