Calcula o valor numérico das expressões
Ainda os números: Matematicamente Falando 8 - Parte 1 Pág. 105 Ex. 7
Enunciado
Calcula o valor numérico das expressões, utilizando, sempre que possível, as regras das potências:
- ${{(0,4)}^{-2}}\times {{4}^{-2}}$
- ${{(0,3)}^{-5}}\div {{(-0,3)}^{-2}}$
- ${{\left( -\frac{1}{4} \right)}^{-3}}\times {{\left( -\frac{1}{4} \right)}^{2}}$
- ${{(-100)}^{-2}}\times {{(0,03)}^{-2}}$
- ${{(0,125)}^{-4}}\div {{\left( \frac{1}{2} \right)}^{-4}}$
Resolução
- Ora,
\[{{(0,4)}^{-2}}\times {{4}^{-2}}={{1,6}^{-2}}={{\left( \frac{16}{10} \right)}^{-2}}={{\left( \frac{8}{5} \right)}^{-2}}={{\left( \frac{5}{8} \right)}^{2}}=\frac{25}{64}\] - Ora,
\[{{(0,3)}^{-5}}\div {{(-0,3)}^{-2}}={{(0,3)}^{-5}}\div {{(+0,3)}^{-2}}={{(0,3)}^{-5-(-2)}}={{\left( \frac{3}{10} \right)}^{-3}}={{\left( \frac{10}{3} \right)}^{3}}=\frac{1000}{27}\] - Ora,
\[{{\left( -\frac{1}{4} \right)}^{-3}}\times {{\left( -\frac{1}{4} \right)}^{2}}={{\left( -\frac{1}{4} \right)}^{-1}}=-4\] - Ora,
\[{{(-100)}^{-2}}\times {{(0,03)}^{-2}}={{(-3)}^{-2}}={{\left( -\frac{1}{3} \right)}^{2}}=\frac{1}{9}\] - Ora,
\[{{(0,125)}^{-4}}\div {{\left( \frac{1}{2} \right)}^{-4}}={{\left( \frac{1}{8} \right)}^{-4}}\div {{\left( \frac{1}{2} \right)}^{-4}}={{\left( \frac{1}{8}\div \frac{1}{2} \right)}^{-4}}={{\left( \frac{1}{8}\times 2 \right)}^{-4}}={{\left( \frac{1}{4} \right)}^{-4}}={{4}^{4}}=256\]
