Reduz a uma só potência

Números inteiros: Matematicamente Falando 7 - Pág. 33 Ex. 5

by AMMA · Published 30 de Outubro de 2012 · Updated 20 de Janeiro de 2022

Enunciado

Reduz a uma só potência:

${\left( { – 2} \right)^2} \times {\left( { – 2} \right)^4}$
${\left( { – 7} \right)^5} \div {7^2}$
${3^2} \times {\left( {{3^3}} \right)^2}$
${21^3} \times {21^2} \times {21^3}$
${\left( { – 3} \right)^3} \div {\left( { – 3} \right)^2}$
$\frac{{{7^2}}}{7}$
${\left( { – 3} \right)^4} \times {\left( { – 3} \right)^3} \div {\left( { – 3} \right)^2}$
${7^4} \times {7^3}$
${\left( { – 3} \right)^3} \times {\left( { – 3} \right)^4} \div \left( { – 3} \right)$
$\frac{{{2^6} \times {{\left( {{2^4}} \right)}^5}}}{{{2^{24}}}}$

Resolução

Ora,
$$\begin{array}{*{20}{l}} {{{\left( { – 2} \right)}^2} \times {{\left( { – 2} \right)}^4}}& = &{{{\left( { – 2} \right)}^6}} \end{array}$$
Ora,
$$\begin{array}{*{20}{l}} {{{\left( { – 7} \right)}^5} \div {7^2}}& = &{{{\left( { – 7} \right)}^5} \div {{\left( { – 7} \right)}^2}} \\ {}& = &{{{\left( { – 7} \right)}^3}} \end{array}$$
Ora,
$$\begin{array}{*{20}{l}} {{3^2} \times {{\left( {{3^3}} \right)}^2}}& = &{{3^2} \times {3^6}} \\ {}& = &{{3^8}} \end{array}$$
Ora,
$$\begin{array}{*{20}{l}} {{{21}^3} \times {{21}^2} \times {{21}^3}}& = &{{{21}^5} \times {{21}^3}} \\ {}& = &{{{21}^8}} \end{array}$$
Ora,
$$\begin{array}{*{20}{l}} {{{\left( { – 3} \right)}^3} \div {{\left( { – 3} \right)}^2}}& = &{{{\left( { – 3} \right)}^1}} \end{array}$$
Ora,
$$\begin{array}{*{20}{l}} {\frac{{{7^2}}}{7}}& = &{\frac{{{7^2}}}{{{7^1}}}} \\ {}& = &{{7^1}} \end{array}$$
Ora,
$$\begin{array}{*{20}{l}} {{{\left( { – 3} \right)}^4} \times {{\left( { – 3} \right)}^3} \div {{\left( { – 3} \right)}^2}}& = &{{{\left( { – 3} \right)}^7} \div {{\left( { – 3} \right)}^2}} \\ {}& = &{{{\left( { – 3} \right)}^5}} \end{array}$$
Ora,
$$\begin{array}{*{20}{l}} {{7^4} \times {7^3}}& = &{{7^7}} \end{array}$$
Ora,
$$\begin{array}{*{20}{l}} {{{\left( { – 3} \right)}^3} \times {{\left( { – 3} \right)}^4} \div \left( { – 3} \right)}& = &{{{\left( { – 3} \right)}^7} \div {{\left( { – 3} \right)}^1}} \\ {}& = &{{{\left( { – 3} \right)}^6}} \end{array}$$
Ora,
$$\begin{array}{*{20}{l}} {\frac{{{2^6} \times {{\left( {{2^4}} \right)}^5}}}{{{2^{24}}}}}& = &{\frac{{{2^6} \times {2^{20}}}}{{{2^{24}}}}} \\ {}& = &{\frac{{{2^{26}}}}{{{2^{24}}}}} \\ {}& = &{{2^2}} \end{array}$$