Question

calcular as potências dos radicais da imagem​

Answer 1

a)

$= (3\sqrt{2} )^{2} \\= 3^{2} \sqrt{2}^{2} \\= 9 . 2\\= 18$

b)

$= (\sqrt[3]{3^{2} } )^{2}\\= \sqrt[3]{3^{2 . 2} } \\= \sqrt[3]{3^{4} } \\= 3.\sqrt[3]{3}$

c)

$= (4\sqrt[4]{2^{2} } )^{2}\\= 4^{2} \sqrt[4]{2^{2.2} }\\= 16 \sqrt[4]{2^{4} }\\= 16 . 2\\= 32$

d)

$= (\sqrt[4]{5^{2} } )^{3}\\= \sqrt[4]{5^{2 . 3} }\\= \sqrt[4]{5^{6} }$

e)

$= (\sqrt[6]{2^{4} } )^{5}\\= \sqrt[6]{2^{4.5} }\\= \sqrt[6]{2^{20} }$

Answer 2

Resposta:

Explicação passo-a-passo:

Para resolvermos estas questões utilizamos essas propriedades abaixo.

$(a\times b)^n=a^n\times b^n\\\\\sqrt[n]{a^n}=a\\\\\sqrt[n]{a^m}=a^{\frac{m}{n}}$

$a)\left(3\sqrt{2}\right)^2=3^2\times (\sqrt{2})^2=9\times 2=\boxed{18}\\b)\left(\sqrt[3]{3^2}\right)^2=\sqrt[3]{3^2}\times \sqrt[3]{3^2}=\sqrt[3]{3^3\times 3}=\boxed{3\sqrt[3]{3}}\\c)\left(4\sqrt[4]{2^2}\right)^2=4^2\times (\sqrt[4]{2^2})^2=16\times 2=\boxed{32}\\d)\left(\sqrt[4]{5^2}\right)^3=\left(5^{\frac{2}{4}}\right)^3=5^{\frac{2}{4}\times 3}=5^{\frac{6}{4}}=\sqrt[4]{5^4\times 5^2}=\boxed{5\sqrt[4]{5^2}}\\e)\left(\sqrt[6]{2^4}\right)^5=\sqrt[6]{2^{20}}=\sqrt[6]{2^{18}\times 2^2}=\boxed{8\sqrt[3]{2}}$

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