Question

Calcule o valor de cada uma das seguintes expressões:
(a)
$( - 1) {}^{ - 3} - ( - 3) {}^{ - 1}$
(b)
$( {2}^{ - 4} + {4}^{ - 2}) {}^{ - 1}$
(c)
${3}^{ - 4} - {3}^{ - 2}$
(d)
$( {8}^{ - 2} - {4}^{3} ) {}^{ - 1}$
​

Answer 1

Resposta e Explicação passo a passo:

$a)(-1)^{-3}-(-3)^{-1}=(-1)^{3}+\frac{1}{3}=-1+\frac{1}{3}=-\frac{3}{3}+\frac{1}{3}=-\frac{2}{3}\\\\b)(2^{-4}+4^{-2})^{-1}=(\frac{1}{2} ^{4}+\frac{1}{4} ^{2})^{-1}=(\frac{1}{16}+\frac{1}{16})^{-1}=(\frac{2}{16})^{-1}=(\frac{16}{2})^{1}=8\\\\c)3^{-4}-3^{-2}=(\frac{1}{3})^{4}-(\frac{1}{3})^{2}=\frac{1}{81}-\frac{1}{9}=\frac{1}{81}-\frac{9}{81}=\frac{-8}{81}\\\\d)(8^{-2}-4^{3})^{-1}=((\frac{1}{8})^{2}-(\frac{1}{4})^{3})^{-1}=(\frac{1}{16}-\frac{1}{64})^{-1}=$

$(\frac{4}{64}-\frac{1}{64})^{-1}=(\frac{3}{64})^{-1}=(\frac{64}{3})^{1}$