Question

Efetue$a) 2^\frac{3}{2}.4^\frac{1}{2}\\-----\\8^\frac{5}{6}\\\\\\b) 1000^{0,666}$

Answer 1

Explicação passo-a-passo:

a)

$\frac{ \sqrt{ {2}^{3} } \times \sqrt{4} }{ \sqrt[6]{ {8}^{5} } } = \frac{ \sqrt{8} \times 2}{ \sqrt[6]{32768} } = \frac{2 \sqrt{2} \times 2 }{4 \sqrt[6]{8} }$

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

b)

${1000}^{ \frac{6}{9} } = {10}^{ {3}^{ \frac{2}{3} } } = {10}^{2} = 100$