Question

Responda as questões seguintes: com cálculos

(a) Resposta =
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(b) Resposta =
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(c) Resposta =
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( OBS: valendo 17 pontos )

Answer 1

Lembrete:

๏ $\sqrt[c]{a^b}=a^{\frac{b}{c}}$
๏ $\frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\cdot \frac{d}{c}$
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$a)\\3^2\cdot \left(2-\left(5^2-\sqrt{36}\right)\right)^2=\\3^2\cdot \left(2-\left(25-6\right)\right)^2=\\3^2\cdot \left(2-19\right)^2=\\3^2\cdot \left(-17\right)^2=\\9\cdot 289=\\\boxed{\bold{2601}}\\\\b)\\128-\sqrt[3]{8}\div \left(7\cdot 3^3-5^3\right)=\\128-\sqrt[3]{8}\div \left(7\cdot 27-125\right)=\\128-\sqrt[3]{8}\div \left(189-125\right)=\\128-2\div 64=\\128-\dfrac{2}{64}=\\\\128-\dfrac{1}{32}=\\\\\dfrac{128\cdot 32}{32}-\dfrac{1}{32}=\\\\\dfrac{4096-1}{32}=\\\\\boxed{\bold{\frac{4095}{32}}}$

$\\c)\\8\sqrt{7}+2\sqrt[6]{7^2}-\sqrt[8]{49^2}\\8\sqrt{7}+2\sqrt[6]{7^2}-\sqrt[8]{7^4}\\8\sqrt{7}+\left(2\cdot 7^{\frac{2}{6}}\right)-7^{\frac{4}{8}}\\8\sqrt{7}+\left(2\cdot 7^{\frac{1}{3}}\right)-7^{\frac{1}{2}}\\\boxed{\bold{8\sqrt{7}+2\sqrt[3]{7}-\sqrt{7}}}$