1. The problem is to understand and simplify the expression $\sqrt[n]{x}$, which represents the $n$-th root of $x$. 2. The $n$-th root of $x$ is defined as the number which, when raised to the power $n$, gives $x$. Mathematically, this is written as: $$\sqrt[n]{x} = x^{\frac{1}{n}}$$ 3. Important rules: - If $n=2$, $\sqrt[n]{x}$ is the square root of $x$. - If $n=3$, it is the cube root, and so on. - For even $n$, $x$ must be non-negative if we are considering real numbers. 4. To simplify or evaluate $\sqrt[n]{x}$, express $x$ in terms of its prime factors or powers, then apply the root: $$\sqrt[n]{x} = x^{\frac{1}{n}}$$ 5. Example: Simplify $\sqrt[3]{8}$. $$\sqrt[3]{8} = 8^{\frac{1}{3}} = (2^3)^{\frac{1}{3}} = 2^{3 \times \frac{1}{3}} = 2^1 = 2$$ 6. Thus, $\sqrt[n]{x}$ is a way to express fractional exponents and roots in algebra.