1. The problem is to understand the expression $\sqrt[n]{x}$, which denotes the $n$-th root of $x$. 2. This means we want to find a number which when raised to the power $n$ equals $x$. 3. In exponential form, the $n$-th root can be written as $x^{\frac{1}{n}}$. 4. So, $\sqrt[n]{x} = x^{\frac{1}{n}}$ means the same as saying $(x^{\frac{1}{n}})^n = x$. 5. This notation generalizes square roots (where $n=2$), cube roots ($n=3$), etc. 6. For example, $\sqrt[3]{8} = 8^{\frac{1}{3}} = 2$ because $2^3 = 8$. The final understanding is that $\sqrt[n]{x}$ represents the $n$-th root of $x$, or equivalently $x^{\frac{1}{n}}$.