Question

Simplifique as expressões em cada caso :
a)$( 3^{n} . 3^{n+1} . 3^{n+2}) : 3^{n+4}$

b)$[ 2^{9} :( 2^{2} . 2 )^{2} ]^{-3}$

c) $[ 3^{4} . ( 3^{3} : 3^{2} )^{-1} ]^{-2}$

Answer 1

a)
$(3^n.3^{n+1}.3^{n+2}):3^{n+4}= \\ \\ (3^{n+n+1+n+2}):3^{n+4}= \\ \\ 3^{3n+3}:3^{n+4} \\ \\ 3^{3n+3-(n+4)}= \\ \\ 3^{3n+3-n-4}= \\ \\ 3^{2n-1$


b)
$[2^9:(2^2.2)^2]^{-3}=$

$[2^9:(2^3)^2]^{-3}=$

$[2^9:2^6]^{-3}= \\ \\ (2^{9-6})^{-3}= \\ \\ (2^3)^{-3}= \\ \\ 2^{-9}$


c)
$[3^4.(3^3:3^2)^{-1}]^{-2}=$

$[3^4.(3^{3-2})^{-1}]^{-2}=$

$(3^4.3^{-1})^{-2}= \\ \\ (3^{4-1})^{-2}= \\ \\ (3^3)^{-2}= \\ \\ 3^{-6}$