1. The problem states the property of radicals: For any real number $n$, the $n$th root of $a^m$ is equal to $a^{m/n}$. 2. The formula used is: $$\sqrt[n]{a^m} = a^{\frac{m}{n}}$$ 3. Explanation: The $n$th root of a number means the value that, when raised to the power $n$, gives the original number. Raising $a$ to the power $m$ and then taking the $n$th root is equivalent to raising $a$ to the power $m/n$. 4. Important rules: - The base $a$ must be a non-negative real number if $n$ is even to keep the root real. - Exponent rules apply: $a^{x} \cdot a^{y} = a^{x+y}$ and $(a^{x})^{y} = a^{xy}$. 5. Example: Simplify $\sqrt[3]{a^6}$. $$\sqrt[3]{a^6} = a^{\frac{6}{3}} = a^2$$ 6. This shows how the root and exponent combine into a single exponent. Final answer: $$\sqrt[n]{a^m} = a^{\frac{m}{n}}$$