Question

Simplifique as expressões.
a) [(3-¹.3³)-¹]-² =
b) (2²/4².8-³)-¹.16 =

Answer 1

$a)\;[(3^{-1}\cdot3^{3})^{-1}]^{-2}=[(3^{-1+3})^{-1}]^{-2}=[(3^{2})^{-1}]^{-2}=[3^{-2}]^{-2}=3^{4}$

$b)\;(\dfrac{2^{2}}{4^{2}}\cdot8^{-3})^{-1}\cdot16=(\dfrac{2^{2}}{(2^{2})^{2}}\cdot(2^{3})^{-3})^{-1}\cdot2^{4}=(\dfrac{2^{2}}{2^{4}}\cdot2^{-9})^{-1}\cdot2^{4}=(2^{2-4}\cdot2^{-9})^{-1}\cdot2^{4}\\\\ =(2^{-2}\cdot2^{-9})^{-1}\cdot2^{4}=(2^{(-2)+(-9)})^{-1}\cdot2^{4}=(2^{-11})^{-1}\cdot2^{4}=2^{11}\cdot2^{4}\\\\=2^{11+4}=2^{15}$