Question

2) Efetua as multiplicações e as divisões com índices diferentes;
a) √2 . ⁴√2=
b) ³√2 . √2=
c) ³√4 : √2=
d) ⁴√7³ . √7=

Answer 1

a)

$\sqrt{2} \times \sqrt[4]{2} = {2}^{ \frac{1}{2} } \times {2}^{ \frac{1}{4} } = {2}^{ \frac{3}{4} } = \sqrt[4]{ {2}^{3} } = \sqrt[4]{8}$

b)

$\sqrt[3]{2} \times \sqrt{2} = {2}^{ \frac{1}{3} } \times {2}^{ \frac{1}{2} } = {2}^{ \frac{5}{6} } = \sqrt[6]{32}$

c)

$\sqrt[3]{4} \div \sqrt{2} = \sqrt[3]{ {2}^{2} } \div \sqrt{2} = {2}^{ \frac{2}{3} } \div {2}^{ \frac{1}{2} } = {2}^{ \frac{7}{6} } = \sqrt[6]{ {2}^{6} \times 2 } = 2\sqrt[6]{2}$

d)

$\sqrt[4]{ {7}^{3} } \times \sqrt{7} = {7}^{ \frac{3}{4} } \times {7}^{ \frac{1}{2} } = {7}^{ \frac{5}{4} } = \sqrt[4]{ {7}^{4} \times7 } = 7 \sqrt[4]{7}$

Espero ter ajudado e

Bons estudos!