Step-by-step explanation:
[tex] \bigg( \frac{3 {a}^{ - 2} {b}^{6} }{2 {a}^{ - 1} {b}^{5} } \bigg)^{2} \\ \\ = \bigg( \frac{3 {b}^{6 - 5} }{2 {a}^{ 2- 1} } \bigg)^{2} \\ \\ = \bigg( \frac{3 {b}^{1} }{2 {a}^{ 1} } \bigg)^{2} \\ \\ = \bigg( \frac{3 {b}}{2 {a}} \bigg)^{2} \\ \\ = \bigg( \frac{3 \times ( - 2)}{2 \times 3} \bigg)^{2} \\ \\ = \bigg( \frac{ - 6}{6} \bigg)^{2} \\ \\ = ( - 1)^{2} \\ \\ \huge\red {\boxed {\therefore \: \bigg( \frac{3 {a}^{ - 2} {b}^{6} }{2 {a}^{ - 1} {b}^{5} } \bigg)^{2} = 1}} \\ [/tex]
