[tex]\displaystyle \sf \boxed{\begin{matrix} \text{Propriedade de potencia\c c\~ao} \\\\ \sf a^{k}\cdot b^{k} = \left(a\cdot b \right)^{k}\end{matrix}} \\\\\\ temos : \\\\ \alpha \cdot 10^{n} = 2^{80}\cdot 5^{76} \ \ ;\ \ 150 < \alpha < 165 \\\\ \text{Fa\c camos } : \\\\ \alpha \cdot 10^{n}= 2^{4}\cdot 2^{76}\cdot 5^{76} \\\\ \alpha \cdot 10^{n}= 2^{4}\cdot (2\cdot 5)^{76}[/tex]
[tex]\displaystyle \sf \alpha \cdot 10^{n}= 16 \cdot 10^{76} \\\\ \alpha\cdot 10^{n} = 16\cdot 10\cdot 10^{75} \\\\ \alpha \cdot 10^{n} = 160\cdot 10^{75} \\\\ Da{\'i}}: \\\\ \alpha = 160 \ \ ;\ \ 10^{n}=10^{75} \to n = 75 \ ; \\\\\ \alpha+n = 160+75 \\\\ \Large\boxed{\sf \ \alpha+n = 235 \ }\checkmark[/tex]
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[tex]\displaystyle \sf \boxed{\begin{matrix} \text{Propriedade de potencia\c c\~ao} \\\\ \sf a^{k}\cdot b^{k} = \left(a\cdot b \right)^{k}\end{matrix}} \\\\\\ temos : \\\\ \alpha \cdot 10^{n} = 2^{80}\cdot 5^{76} \ \ ;\ \ 150 < \alpha < 165 \\\\ \text{Fa\c camos } : \\\\ \alpha \cdot 10^{n}= 2^{4}\cdot 2^{76}\cdot 5^{76} \\\\ \alpha \cdot 10^{n}= 2^{4}\cdot (2\cdot 5)^{76}[/tex]
[tex]\displaystyle \sf \alpha \cdot 10^{n}= 16 \cdot 10^{76} \\\\ \alpha\cdot 10^{n} = 16\cdot 10\cdot 10^{75} \\\\ \alpha \cdot 10^{n} = 160\cdot 10^{75} \\\\ Da{\'i}}: \\\\ \alpha = 160 \ \ ;\ \ 10^{n}=10^{75} \to n = 75 \ ; \\\\\ \alpha+n = 160+75 \\\\ \Large\boxed{\sf \ \alpha+n = 235 \ }\checkmark[/tex]
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