1. **State the problem:** Evaluate the expression $$(5^{-1} \times 2^{-1}) \times 6^{-1}$$. 2. **Recall the meaning of negative exponents:** For any nonzero number $a$, $a^{-1} = \frac{1}{a}$. 3. **Rewrite each term with negative exponents:** $$5^{-1} = \frac{1}{5}, \quad 2^{-1} = \frac{1}{2}, \quad 6^{-1} = \frac{1}{6}$$ 4. **Substitute these into the expression:** $$\left( \frac{1}{5} \times \frac{1}{2} \right) \times \frac{1}{6}$$ 5. **Multiply the fractions inside the parentheses:** $$\frac{1}{5} \times \frac{1}{2} = \frac{1}{10}$$ 6. **Now multiply by $\frac{1}{6}$:** $$\frac{1}{10} \times \frac{1}{6} = \frac{1}{60}$$ 7. **Final answer:** $$\boxed{\frac{1}{60}}$$