Question

Simplificando a expressão

Answer 1

Olá!

Essa é uma questão que exige conhecimento das propriedades de potências.
${[}2^9\div(2^2\cdot2)^3{]}^{-3}=\\\\{[}2^9\div(2^2\cdot2^1)^3{]}^{-3}=\\\\{[}2^9\div(2^{2+1})^3{]}^{-3}=\\\\{[}2^9\div(2^3)^3{]}^{-3}=\\\\{[}2^9\div2^{3\cdot3}{]}^{-3}=\\\\{[}2^9\div2^9{]}^{-3}=\\\\{[}2^{9-9}{]}^{-3}=\\\\{[}2^0{]}^{-3}=\\\\{[}1{]}^{-3}=1\\\\\\\boxed{{[}2^9\div(2^2\cdot2)^3{]}^{-3}=1}$

Bons estudos!