Question

resolva as potências abaixo

a) (³√2)⁶
b) (√5)⁴
c) (√7) ⁷

Answer 1

Explicação passo-a-passo:

a)

$\sf (\sqrt[3]{2})^6$

$\sf =\sqrt[3]{2^6}$

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

$\sf =2^2$

$\sf =\red{4}$

b)

$\sf (\sqrt{5})^4$

$\sf =\sqrt{5^4}$

$\sf =\sqrt{(5^2)^2}$

$\sf =5^2$

$\sf =\red{25}$

c)

$\sf (\sqrt{7})^7$

$\sf =\sqrt{7^7}$

$\sf =\sqrt{7^6\cdot7}$

$\sf =\sqrt{(7^3)^2\cdot7}$

$\sf =7^3\sqrt{7}$

$\sf =\red{343\sqrt{7}}$

Answer 2

Oie, Td Bom?!

a)

$= \sqrt[3]{2} {}^{6}$

$= \sqrt[3 \div 3]{2} {}^{6 \div 3}$

$= \sqrt[1]{2} {}^{2}$

$= 2 {}^{2}$

$= 2 \: . \: 2$

$= 4$

b)

$= \sqrt{5} {}^{4}$

$= \sqrt[2 \div 2]{5} {}^{4 \div 2}$

$= \sqrt[1]{5} {}^{2}$

$= 5 {}^{2}$

$= 5 \: . \: 5$

$= 25$

c)

$= \sqrt{7} {}^{7}$

$= \sqrt{7 {}^{7} }$

$= \sqrt{7 {}^{6} \: . \: 7}$

$= \sqrt{7 {}^{6} } \sqrt{7}$

$= 7 {}^{3} \: . \: \sqrt{7}$

$= 343 \sqrt{7}$

Att. Makaveli1996