Determina
Ainda os números: Matematicamente Falando 8 - Parte 1 Pág. 105 Ex. 8
Enunciado
Determina:
- ${{3}^{3}}\div {{3}^{6}}+{{\left( {{3}^{2}} \right)}^{-1}}$
- ${{10}^{0}}+{{7}^{-1}}\times {{7}^{2}}\div {{7}^{-3}}$
- ${{({{4}^{0}}-{{4}^{-1}}+{{4}^{-2}})}^{-6}}\div {{\left( \frac{16}{13} \right)}^{5}}$
Resolução
- Ora,
\[{{3}^{3}}\div {{3}^{6}}+{{\left( {{3}^{2}} \right)}^{-1}}={{3}^{-3}}+{{3}^{-2}}={{\left( \frac{1}{3} \right)}^{3}}+{{\left( \frac{1}{3} \right)}^{2}}=\frac{1}{27}+\frac{1}{9}=\frac{1}{27}+\frac{3}{27}=\frac{4}{27}\] - Ora,
\[{{10}^{0}}+{{7}^{-1}}\times {{7}^{2}}\div {{7}^{-3}}=1+{{7}^{1}}\div {{7}^{-3}}=1+{{7}^{4}}=1+2401=2402\] - Ora,
\[\begin{array}{*{35}{l}}
{{({{4}^{0}}-{{4}^{-1}}+{{4}^{-2}})}^{-6}}\div {{\left( \frac{16}{13} \right)}^{5}} & = & {{(1-\frac{1}{4}+\frac{1}{16})}^{-6}}\div {{\left( \frac{16}{13} \right)}^{5}} \\
{} & = & {{(\frac{16}{16}-\frac{4}{16}+\frac{1}{16})}^{-6}}\div {{\left( \frac{16}{13} \right)}^{5}} \\
{} & = & {{\left( \frac{13}{16} \right)}^{-6}}\div {{\left( \frac{13}{16} \right)}^{-5}} \\
{} & = & {{\left( \frac{13}{16} \right)}^{-1}} \\
{} & = & \frac{16}{13} \\
\end{array}\]
