Question

SIMPLIFIQUE AS EXPRESSÕES EM UMA SÓ POTÊNCIA

Answer 1

$(2^3.4^2.16)^{-1} .32= \\ \\ =(2^3.(2^2)^2.2^4)^{-1} .2^5= \\ \\ =(2^3.2^4.2^4)^{-1} .2^5= \\ \\ =( 2^{3+4+4} )^{-1} .2^5= \\ \\ = (2^{11} )^{-1} .2^5= \\ \\ = 2^{-11} .2^5= \\ \\ =2^{-11+5} = \\ \\ = 2^{-6} \\ \\ \\ \\ ( \frac{3^2}{9^2} . 27^{-3} )^2. 3^{14} = \\ \\ =( \frac{3^2}{ (3^{2} )^2} . (3^{3} )^{-3} )^2. 3^{14}= \\ \\ =( \frac{3^2}{ (3^{4} )} . 3^{-9} )^2. 3^{14}= \\ \\ = ( 3^({2-4}). 3^{-9} )^{2} . 3^{14} = \\ \\ = (3^{-2}. 3^{-9} ) ^{2} . 3^{14} =$
$=( 3^{-11} )^{2} . 3^{14} = 3^{-22} . 3^{14} = 3^{-8}$