Answer:
[tex] \boxed{part \: 1.} \\ \boxed{ \: ans = - 8a^{5} b ^{2}} \\ ........................................................\\ \\ \boxed{part \: 2.} \\ \boxed{ \: ans = \frac{6x ^{3} }{y ^{3}} } \: or \: (\frac{6x}{y} ) ^{3} \\ \\ ........................................................\\ \boxed{part \: 3.} \\ \: \boxed{ans =\frac{8a^{6}}{27b^{3}} } \\ ........................................................ \\ \boxed{part \: 4.} \\ \\ \boxed{ \: ans = 6^{3}g^{15}h{}^{ - 12} } \\ ........................................................[/tex]
Step-by-step explanation:
[tex] \boxed{part \: 1.} \\ ........................................................ \\ (2a ^{3} b ^{ - 2})( - 4a^{2}b^{4}) \to \\ \boxed{ \: ans = - 8a^{5} b ^{2}} \\ ........................................................\\ \\ \boxed{part \: 2.} \\ ........................................................\: \\ \frac{12x^{4}y^{2}}{2xy^{5}} \to \\ \boxed{ \: ans = \frac{6x ^{3} }{y ^{3}} }= (\frac{6x}{y} ) ^{3} \\ \\ ........................................................\\ \boxed{part \: 3.} \\ ........................................................\\ \: ( \frac{2a^{2}}{3b} )^{3} \to \: \\ \frac{2^{3}a^{6}}{3^{3}b^{3}} =\frac{8a^{6}}{27b^{3}} \\ \boxed{ans =\frac{8a^{6}}{27b^{3}} } \\ ........................................................\\ \boxed{part \: 4.} \\ ........................................................ \\ (6g^{5}h^{ - 4})^{3} \to\\ \boxed{ \: ans = 6^{3}g^{15}h{}^{ - 12} } \\ ........................................................[/tex]
