Question

Calcule o valor das expressões a) 81 1/4 + 81 1/4= b) 8 1/3 . 125 2/3= c) 343 4/3 : 49⁰,⁵= d) 36 3/2 - 32 2/5=

Answer 1

Explicação passo-a-passo:

a) $\sf 81^{\frac{1}{4}}+81^{\frac{1}{4}}$

$\sf =\sqrt[4]{81}+\sqrt[4]{81}$

$\sf =\sqrt[4]{3^4}+\sqrt[4]{3^4}$

$\sf =3+3$

$\sf =6$

b) $\sf 8^{\frac{1}{3}}\cdot125^{\frac{2}{3}}$

$\sf =\sqrt[3]{8}\cdot\sqrt[3]{125^2}$

$\sf =\sqrt[3]{8}\cdot\sqrt[3]{(5^3)^2}$

$\sf =\sqrt[3]{2^3}\cdot\sqrt[3]{(5^2)^3}$

$\sf =2\cdot5^2$

$\sf =2\cdot25$

$\sf =50$

c) $\sf 343^{\frac{4}{3}}\div49^{0,5}$

$\sf =\sqrt[3]{343^4}\div49^{\frac{1}{2}}$

$\sf =\sqrt[3]{(7^3)^4}\cdot\sqrt{49}$

$\sf =\sqrt[3]{(7^4)^3}\div\sqrt{7^2}$

$\sf =7^4\div7$

$\sf =7^3$

$\sf =343$

d) $\sf 36^{\frac{3}{2}}-32^{\frac{2}{5}}$

$\sf =\sqrt{36^3}-\sqrt[5]{32^2}$

$\sf =\sqrt{(6^2)^3}-\sqrt[5]{(2^5)^2}$

$\sf =\sqrt{(6^3)^2}-\sqrt[5]{(2^2)^5}$

$\sf =6^3-2^2$

$\sf =216-4$

$\sf =212$

Answer 2

Resposta:

A)= 6

B)=50

C)=7³

D)=212

espero ter ajudado