1. We are asked to simplify the expression $$18^{-\frac{1}{2}} \cdot 2^{-\frac{1}{2}}$$. 2. Recall the rule for exponents: $$a^{-b} = \frac{1}{a^b}$$ and the product rule: $$a^m \cdot b^m = (ab)^m$$. 3. Apply the product rule to combine the terms since both have the same exponent $$-\frac{1}{2}$$: $$18^{-\frac{1}{2}} \cdot 2^{-\frac{1}{2}} = (18 \cdot 2)^{-\frac{1}{2}}$$ 4. Multiply inside the parentheses: $$18 \cdot 2 = 36$$ 5. So the expression becomes: $$36^{-\frac{1}{2}}$$ 6. Using the negative exponent rule: $$36^{-\frac{1}{2}} = \frac{1}{36^{\frac{1}{2}}}$$ 7. The exponent $$\frac{1}{2}$$ means square root, so: $$\frac{1}{\sqrt{36}}$$ 8. Calculate the square root: $$\sqrt{36} = 6$$ 9. Final simplified expression: $$\frac{1}{6}$$