Answer:
[tex] {( \frac{ {2x}^{4} {y}^{4} }{ {4x}^{2} } )}^{3} \\ [/tex]
open the bracket:
[tex] = \frac{ {2x}^{(4 \times 3)} {y}^{(4 \times 3)} }{ {4x}^{(2 \times 3)} } \\ [/tex]
simplify:
[tex] = \frac{ {2x}^{12} {y}^{12} }{ {4x}^{6} } \\ [/tex]
group x terms together:
[tex] = ( \frac{ {2x}^{12} }{ {4x}^{6} } ) \times {y}^{12} \\ \\ = (\frac{ {x}^{(12 - 6)} }{2} ) \times {y}^{12} \\ \\ = \frac{ {x}^{6} }{2} \times {y}^{12} [/tex]
factorise out power 6:
[tex] { \boxed{= \frac{ {(xy {}^{2}) }^{6} }{2} }}\\ [/tex]
