1. The problem is to simplify or understand the expression $\sqrt[b]{2}$, which is the $b$-th root of 2. 2. The $b$-th root of a number $a$ is defined as the number which, when raised to the power $b$, equals $a$. Mathematically, $\sqrt[b]{a} = a^{\frac{1}{b}}$. 3. Applying this to our problem, we have: $$\sqrt[b]{2} = 2^{\frac{1}{b}}$$ 4. This expression means that if you raise $2^{\frac{1}{b}}$ to the power $b$, you get 2: $$\left(2^{\frac{1}{b}}\right)^b = 2^{\frac{b}{b}} = 2^1 = 2$$ 5. Therefore, $\sqrt[b]{2}$ is simply $2$ raised to the power of $\frac{1}{b}$, which is the principal $b$-th root of 2. Final answer: $$\sqrt[b]{2} = 2^{\frac{1}{b}}$$