1. The problem is to understand and express the general form of the $n$th root of $x$, written as $\sqrt[n]{x}$. 2. The $n$th root of a number $x$ is the number that, when raised to the power $n$, gives $x$. This can be expressed using exponents as: $$\sqrt[n]{x} = x^{\frac{1}{n}}$$ 3. Important rules: - If $n$ is even, $x$ must be non-negative for the root to be a real number. - If $n$ is odd, $x$ can be any real number. 4. For example, the square root ($n=2$) is $\sqrt{x} = x^{\frac{1}{2}}$. 5. This notation generalizes to any positive integer $n$. 6. Therefore, the $n$th root of $x$ is simply $x$ raised to the power of $\frac{1}{n}$.