Question

1) calcule o valor numèrico de cada expressão:
$a)( - 2 - \frac{2}{5} ) \times ( - \frac{3}{4}) ^{2}$
$b)1 - ( \frac{1}{3} ) ^{3} \div ( \frac{1}{2} - 1) ^{2}$
$c)(5 - \frac{1}{2}) ^{2} \div ( \frac{1}{2} - 2) ^{3}$
2) calcule as expressões abaixo:
$a) \frac{3}{4} \div ( - \frac{2}{3} )$
$b) \frac{4}{3} \times ( \frac{3}{5} - \frac{1}{2} )$
$c) {3}^{2} + {2}^{1} + {3}^{1} + {2}^{2}$
$d)( \frac{1}{2} ) ^{2} + ( \frac{1}{3} ) ^{1} + ( \frac{1}{3}) ^{2}$
$e)( \frac{2}{3}) ^{2} \times ( \frac{1}{5} - \frac{4}{7} )$
3)qual é o valor da expressão:
$\sqrt \frac{4}{25} - \sqrt \frac{1}{9} + \sqrt \frac{9}{25} - \sqrt \frac{4}{9}$

4) calcule:
$a) \sqrt \frac{121}{100} + \sqrt \frac{81}{25}$
$b) \sqrt \frac{49}{64} - \sqrt \frac{625}{144} + \sqrt \frac{1}{36} - \sqrt \frac{16}{9}$
​

Answer 1

Olá!

Questão 1)

Letra a)

$\left(\dfrac{2}{1} -\dfrac{2}{5} \right)\times\left(-\dfrac{3}{4} \right)^{2}\\ \\ \\ \\ \left(\dfrac{10-2}{5} \right)\times\left(-\dfrac{3}{4} \right)^{2}\\ \\ \\ \\ \left(\dfrac{8}{5} \right)\times\left(\dfrac{9}{16} \right)=\dfrac{72}{80}~~~simplificar~~por~~8 \\ \\ \\ \\ \boxed{\dfrac{9}{10} }$

Letra b)

$\dfrac{1}{1} -\left(\dfrac{1}{3} \right)^{3}~\div~\left(\dfrac{1}{2} -\dfrac{1}{1} \right)^{2}\\ \\ \\ \\ \dfrac{1}{1}-\left(\dfrac{1}{3} \right)^{3}~\div~\left(\dfrac{1-2}{2} \right)^{2}\\ \\ \\ \\ \dfrac{1}{1}-\left(\dfrac{1}{3} \right)^{3}~\div~\left(-\dfrac{1}{2} \right)^{2}\\ \\ \\ \\ \left(\dfrac{1}{1}-\dfrac{1}{27}\right)~~\div~~\dfrac{1}{4}\\ \\ \\ \\ \left(\dfrac{27-1}{27}\right)~~\div~~\dfrac{1}{4}\\ \\ \\ \\ \dfrac{1}{27}~~\div~~\dfrac{1}{4}\\ \\ \\ \\ \dfrac{1}{27}~\times~\dfrac{4}{1}$

$\boxed{\dfrac{4}{27}}$

Letra c)

$\left(\dfrac{5}{1}-\dfrac{1}{2} \right)^{2}~\div~\left(\dfrac{1}{2}-\dfrac{2}{1} \right)^{3}\\ \\ \\ \\ \left(\dfrac{10-1}{2} \right)^{2}~\div~\left(\dfrac{1-4}{2} \right)^{3}\\ \\ \\ \\ \left(\dfrac{9}{2} \right)^{2}~\div~\left(-\dfrac{3}{2} \right)^{3}\\ \\ \\ \\ \dfrac{81}{4}~~ \div~~ \left(-\dfrac{27}{8}\right)\\ \\ \\ \\ \dfrac{81}{4}~\times~\left(-\dfrac{8}{27}\right)\\ \\ \\ \\ -\dfrac{648}{108} \\ \\ \\ \\ \boxed{-6}$

Questão 2)

Letra a)

$\dfrac{3}{4}~~\div~~\left(-\dfrac{2}{3} \right)\\ \\ \\ \\ \dfrac{3}{4}~~\times~\left(-\dfrac{3}{2} \right)\\ \\ \\ \\ \boxed{-\dfrac{9}{8}}$

Letra b)

$\dfrac{4}{3} ~\times~\left(\dfrac{3}{5} -\dfrac{1}{2} \right)\\ \\ \\ \\ \dfrac{4}{3} ~\times~\left(\dfrac{6-5}{10} \right)\\ \\ \\ \\ \dfrac{4}{3}~\times~\dfrac{1}{10}~~=~~\dfrac{4}{30}~~simplificar~~por~~2\\ \\ \\ \\ \boxed{\dfrac{2}{15}}$

Letra c)

$3^{2} +2^{1} +3^{1} +2^{2} \\ \\ 9+2+3+4\\ \\ \boxed{18}$

Letra d)

$\left(\dfrac{1}{2} \right)^{2}+\left(\dfrac{1}{3} \right)^{1}+\left(\dfrac{1}{3} \right)^{2}\\ \\ \\ \\\dfrac{1}{4}+\dfrac{1}{3}+\dfrac{1}{9}\\ \\ \\ \\ \dfrac{9+12+4}{36} \\ \\ \\ \\ \boxed{\dfrac{25}{36}}$

Letra e)

$\left(\dfrac{2}{3}\right)^{2}\times\left(\dfrac{1}{5}-\dfrac{4}{7} \right)\\ \\ \\\\ \left(\dfrac{2}{3}\right)^{2}\times\left(\dfrac{7-20}{35} \right) \\ \\ \\ \\ \dfrac{4}{9}~\times~\left(-\dfrac{13}{35}\right)\\ \\ \\ \\ \boxed{-\dfrac{52}{315}}$

Questão 3)

$\sqrt{\dfrac{4}{25} } ~-~\sqrt{\dfrac{1}{9} }~+~ \sqrt{\dfrac{9}{25} }~ -~\sqrt{\dfrac{4}{9} }\\ \\ \\ \\ \dfrac{2}{5}~-~\dfrac{1}{3}~+~\dfrac{3}{5}~-~\dfrac{2}{3}\\ \\ \\ \\ \dfrac{6-5+9-10}{15}~~=~~\dfrac{0}{15}\\ \\ \\ \\ \boxed{0}$

Questão 4)

Letra a)

$\sqrt{\dfrac{121}{100} } ~+~\sqrt{\dfrac{81}{25} } \\ \\ \\ \\ \dfrac{11}{10}~+~\dfrac{9}{5}\\ \\ \\ \\ \dfrac{11+18}{10}\\ \\ \\ \\ \boxed{\dfrac{29}{10}}$

Letra b)

$\sqrt{\dfrac{49}{64} } ~-~\sqrt{\dfrac{625}{144} }~+~\sqrt{\dfrac{1}{36} } ~-~\sqrt{\dfrac{16}{9} }\\ \\ \\ \\ \\\dfrac{7}{8}~-~\dfrac{25}{12}~+~\dfrac{1}{6}~-~\dfrac{4}{3}\\ \\ \\ \\ \dfrac{21-50+4-32\\ }{24}\\ \\ \\ \\ \boxed{-\dfrac{57}{24}}$

:)