Calcula, usando, se possível, as regras operatórias das potências
Números inteiros: Matematicamente Falando 7 - Pág. 33 Ex. 6
Enunciado
Calcula, usando, se possível, as regras operatórias das potências:
- ${2^3} \times {2^4}$
- ${\left( {{5^4}} \right)^3} \div {5^{10}}$
- ${\left( { – 4} \right)^6} \div {2^6}$
- $\left( { – 81} \right) \div {\left( { – 3} \right)^4}$
- ${2^3} \times {\left( { – 2} \right)^4}$
- ${\left( { – 3} \right)^5} \div {3^5}$
- ${\left( { – 1} \right)^{100}} \times {\left( { – 1} \right)^2}$
- ${2^3} + {2^4}$
- ${3^2} – \left( { – {3^3}} \right)$
- ${\left( { – 2} \right)^2} + {\left( { – 3} \right)^2}$
- ${\left( { – 2} \right)^2} \times {\left( { – 3} \right)^2}$
- ${3^2} \times {\left( { – 3} \right)^3}$
Resolução
- Ora,
$$\begin{array}{*{20}{l}} {{2^3} \times {2^4}}& = &{{2^7}} \\ {}& = &{128} \end{array}$$ - Ora,
$$\begin{array}{*{20}{l}} {{{\left( {{5^4}} \right)}^3} \div {5^{10}}}& = &{{5^{12}} \div {5^{10}}} \\ {}& = &{{5^2}} \\ {}& = &{25} \end{array}$$ - Ora,
$$\begin{array}{*{20}{l}} {{{\left( { – 4} \right)}^6} \div {2^6}}& = &{{{\left( { – 2} \right)}^6}} \\ {}& = &{64} \end{array}$$ - Ora,
$$\begin{array}{*{20}{l}} {\left( { – 81} \right) \div {{\left( { – 3} \right)}^4}}& = &{ – {{\left( { + 3} \right)}^4} \div {{\left( { – 3} \right)}^4}} \\ {}& = &{ – {{\left( { – 1} \right)}^4}} \\ {}& = &{ – 1} \end{array}$$ - Ora,
$$\begin{array}{*{20}{l}} {{2^3} \times {{\left( { – 2} \right)}^4}}& = &{{2^3} \times {2^4}} \\ {}& = &{{2^7}} \\ {}& = &{128} \end{array}$$ - Ora,
$$\begin{array}{*{20}{l}} {{{\left( { – 3} \right)}^5} \div {3^5}}& = &{{{\left( { – 1} \right)}^5}} \\ {}& = &{ – 1} \end{array}$$ - Ora,
$$\begin{array}{*{20}{l}} {{{\left( { – 1} \right)}^{100}} \times {{\left( { – 1} \right)}^2}}& = &{{{\left( { – 1} \right)}^{102}}} \\ {}& = &1 \end{array}$$ - Ora,
$$\begin{array}{*{20}{l}} {{2^3} + {2^4}}& = &{8 + 16} \\ {}& = &{24} \end{array}$$ - Ora,
$$\begin{array}{*{20}{l}} {{3^2} – \left( { – {3^3}} \right)}& = &{9 – \left( { – 27} \right)} \\ {}& = &{9 + 27} \\ {}& = &{36} \end{array}$$ - Ora,
$$\begin{array}{*{20}{l}} {{{\left( { – 2} \right)}^2} + {{\left( { – 3} \right)}^2}}& = &{4 + 9} \\ {}& = &{13} \end{array}$$ - Ora,
$$\begin{array}{*{20}{l}} {{{\left( { – 2} \right)}^2} \times {{\left( { – 3} \right)}^2}}& = &{{6^2}} \\ {}& = &{36} \end{array}$$ - Ora,
$$\begin{array}{*{20}{l}} {{3^2} \times {{\left( { – 3} \right)}^3}}& = &{{{\left( { – 3} \right)}^2} \times {{\left( { – 3} \right)}^3}} \\ {}& = &{{{\left( { – 3} \right)}^5}} \\ {}& = &{ – 243} \end{array}$$
