Let us find out the values: \big\{(125)^{-2} \times (16)^ \frac{-3}{2}\big\}^{ \frac{-1}{6}}

= \big\{(5^3)^{-2} \times (2^4)^{-\frac{3}{2}}\big\} ^{ -\frac{1}{6} }

= \big\{(5)^{3 \times -2} \times (2^4)^{-\frac{3}{2}}\big\} ^{ -\frac{1}{6}}

= \big\{5^{-6} \times 2{-6}\big\}^{-\frac{1}{6}}

= \big\{(5 \times 2 ^{-6} \big\}^{-\frac{1}{6}}

= (5 \times 2)^{-6 \times -\frac{1}{6} }

= (10)¹ = 10 Ans.