[tex]~\huge\mid{\boxed{\bf{\blue{Matem\acute{a}tica}}}\mid}[/tex]
[tex](( \frac{ {10}^{7} \times {10}^{13} }{ {10}^{12} \times {10}^{5} \times {10}^{2} } {)}^{4} {)}^{5} + ( \frac{ {10}^{ - 4} \times {10}^{6} }{ {10}^{3} \times {10}^{ - 11} } {)}^{2} [/tex]
• Usando a propriedade de potência [tex]\color{green} {{ }}( {2}^{2} {)}^{2} = {2}^{2 \times 2} = {2}^{ {4}^{} } [/tex]
[tex]( \frac{ {10}^{7} \times {10}^{13} }{ {10}^{12} \times {10}^{5} \times {10}^{2} } {)}^{4 \times 5} {}^{} + ( \frac{ {10}^{ - 4} \times {10}^{6} }{ {10}^{3} \times {10}^{ - 11} } {)}^{2} [/tex]
[tex]( \frac{ {10}^{7} \times {10}^{13} }{ {10}^{12} \times {10}^{5} \times {10}^{2} } {)}^{20} {}^{} + ( \frac{ {10}^{ - 4} \times {10}^{6} }{ {10}^{3} \times {10}^{ - 11} } {)}^{2} [/tex]
• Use a propriedade [tex]\color{green} {{ }} {2}^{2} \times {2}^{2} = {2}^{2 + 2} = {2}^{4} [/tex]
[tex](\frac{ {10}^{7 + 13} }{ {10}^{12 + 5 + 2} } {)}^{20} + ( \frac{ {10}^{ - 4 + 6} }{ {10}^{3 - 11} } {)}^{2} [/tex]
[tex](\frac{ {10}^{7 + 13} }{ {10}^{12 + 5 + 2} } {)}^{20} + ( \frac{ {10}^{ 2} }{ {10}^{ - 8} } {)}^{2} [/tex]
[tex](\frac{ {10}^{20} }{ {10}^{19} } {)}^{20} + ( \frac{ {10}^{ 2} }{ {10}^{ - 8} } {)}^{2} [/tex]
• Use a propriedade [tex]\color{green} {{ }} \frac{ {2}^{2} }{ {2}^{2} } = {2}^{2 - 2} = {2}^{0} [/tex]
[tex](\frac{ {10}^{20} }{ {10}^{19} } {)}^{20} + ( {10}^{2 - ( - 8)} {)}^{2} [/tex]
• Faça o jogo de sinal: (-) × (-) = (+)
[tex]( \frac{ {10}^{20} }{ {10}^{19} } {)}^{20} + ( {10}^{2 + 8} {)}^{2} [/tex]
[tex]( \frac{ {10}^{20} }{ {10}^{19} } {)}^{20} + ( {10}^{10} {)}^{2} [/tex]
[tex]( {10}^{20 - 19} {)}^{20} + ( {10}^{10} {)}^{2} [/tex]
[tex]( {10}^{1} {)}^{20} + ( {10}^{10} {)}^{2} [/tex]
[tex] {10}^{1 \times 20} + ( {10}^{10} {)}^{2} [/tex]
[tex] {10}^{20} + {10}^{10 \times 2} [/tex]
[tex] {10}^{20} + {10}^{20} [/tex]
• Acrescente o coeficiente 1
[tex]1 \times {10}^{20} + 1 \times {10}^{20} [/tex]
[tex](1 + 1) \times {10}^{20} [/tex]
Resposta: [tex]\color{green} \boxed{{ 2 \times {10}^{20} }}[/tex]
[tex]{\huge\boxed { {\bf{E}}}\boxed { \red {\bf{a}}} \boxed { \blue {\bf{s}}} \boxed { \gray{\bf{y}}} \boxed { \red {\bf{}}} \boxed { \orange {\bf{M}}} \boxed {\bf{a}}}{\huge\boxed { {\bf{t}}}\boxed { \red {\bf{h}}}}[/tex]
