#### Answer

This expression cannot be simplified by the product rule.

#### Work Step by Step

The product rule for radicals tells us that $\sqrt[n] a\times\sqrt[n] b=\sqrt[n] ab$ (when $\sqrt[n] a$ and $\sqrt[n] b$ are real numbers and $n$ is a natural number). That is, the product of two nth roots is the nth root of the product.
Therefore, $\sqrt[5] 8 \times\sqrt[6] 12$ cannot be simplified using the product rule because the indexes (5 and 6) are different.