1. **State the problem:** Simplify the expression $$x^{-\frac{17}{6}} \times x^{-\frac{11}{5}}$$ and write the answer in the form $$A$$ or $$\frac{A}{B}$$ where $$A$$ and $$B$$ are constants or variable expressions with no common variables, and all exponents are positive. 2. **Recall the rule for multiplying powers with the same base:** When multiplying expressions with the same base, add the exponents: $$x^a \times x^b = x^{a+b}$$ 3. **Apply the rule:** $$x^{-\frac{17}{6}} \times x^{-\frac{11}{5}} = x^{-\frac{17}{6} - \frac{11}{5}}$$ 4. **Find a common denominator to add the exponents:** The denominators are 6 and 5, so the common denominator is 30. Convert each fraction: $$-\frac{17}{6} = -\frac{17 \times 5}{6 \times 5} = -\frac{85}{30}$$ $$-\frac{11}{5} = -\frac{11 \times 6}{5 \times 6} = -\frac{66}{30}$$ 5. **Add the exponents:** $$-\frac{85}{30} - \frac{66}{30} = -\frac{85 + 66}{30} = -\frac{151}{30}$$ 6. **Rewrite the expression:** $$x^{-\frac{151}{30}}$$ 7. **Make the exponent positive:** Recall that $$x^{-a} = \frac{1}{x^a}$$ for positive $$a$$. So, $$x^{-\frac{151}{30}} = \frac{1}{x^{\frac{151}{30}}}$$ **Final answer:** $$\boxed{\frac{1}{x^{\frac{151}{30}}}}$$