1. The problem asks whether for any real number $n$, the equation $$\sqrt[n]{ab} = \sqrt[n]{a} \times \sqrt[n]{b}$$ is true. 2. The formula used here is the property of radicals: $$\sqrt[n]{x} = x^{\frac{1}{n}}$$. 3. Using this, we rewrite the terms: $$\sqrt[n]{ab} = (ab)^{\frac{1}{n}}$$ $$\sqrt[n]{a} \times \sqrt[n]{b} = a^{\frac{1}{n}} \times b^{\frac{1}{n}}$$ 4. By the laws of exponents, multiplying powers with the same exponent means: $$a^{\frac{1}{n}} \times b^{\frac{1}{n}} = (ab)^{\frac{1}{n}}$$ 5. Therefore, $$\sqrt[n]{ab} = \sqrt[n]{a} \times \sqrt[n]{b}$$ holds true for any real number $n$ where the roots are defined (i.e., $a$ and $b$ are nonnegative if $n$ is even). 6. Important note: This property holds when $a$ and $b$ are nonnegative if $n$ is even, because even roots of negative numbers are not real. Final answer: True.