Question

Efetue as operações indicadas a seguir.

a) 3∛2 x 9∛5

b) 20∛8 : 5∛16

c) 7√11 x 5∜3

d) 2√5 x 3∛5

Answer 1

Olá, Gustavo.

a) 3∛2 × 9∛5 = $3\times9\times\sqrt[3]{2\cdot5}=27\sqrt[3]{10}$

b) 20∛8 : 5∛16 = 
$=\frac{20\sqrt[3]{8}}{5\sqrt[3]{16}}=\frac{20}{5}\cdot\sqrt[3]{\frac{8}{16}}=4\sqrt[3]{\frac{1}{2}}=4\frac{1}{\sqrt[3]{2}}=4\cdot\frac{1}{\sqrt[3]{2}}\cdot\frac{\sqrt[3]{2^2}}{\sqrt[3]{2^2}}=4\cdot\frac{\sqrt[3]{4}}{\sqrt[3]{2^3}}=\\=4\cdot\frac{\sqrt[3]{4}}{2}=2\sqrt[3]{4}$

c) 7√11 × 5∜3 = $7\sqrt[4]{11^2}\times5\sqrt[4]3=7\times5\times\sqrt[4]{11^2\cdot3}=35\sqrt[4]{363}$

d) 2√5 × 3∛5  = $2\sqrt[6]{5^3}\times3\sqrt[6]{5^2}=2\times3\times\sqrt[6]{5^3\cdot5^2}=6\sqrt[6]{5^5}=6\sqrt[6]{3125}$