Question

1. Utilize as propriedades e calcule.

a)⁸√99⁸

b)√³√64

c)⁴√3×⁴√27

d)⁷√(-27)⁷

e)⁵√⁵√-1

f)
$\sqrt{ \frac{16}{49} }$
g)√√81

h)³√⁴√2¹²

i)√³√⁴√3⁴⁸
​

Answer 1

Resposta:

1 -

$a) \sqrt[8]{ {99}^{8} } = {99}^{ \frac{8}{8} } = 99$

$b) \sqrt{ \sqrt[3]{64} } = \sqrt[2.3]{64} = \sqrt[6]{64} = 2$

$c) \sqrt[4]{3} \: . \: \sqrt[4]{27} = \sqrt[4]{3.27} = \sqrt[4]{81} = 3$

$d) \sqrt[7]{ {( - 27)}^{7} } = {( - 27)}^{ \frac{7}{7} } = - 27$

$e){ \sqrt[5]{ \sqrt[5]{ - 1} } } = \sqrt[5.5]{ - 1} = \sqrt[25]{ - 1} = - 1$

$f) \sqrt{ \frac{16}{49} } = \frac{ \sqrt{16} }{ \sqrt{49} } = \frac{4}{7}$

$g) \sqrt{ \sqrt{81} } = \sqrt[2.2]{81} = \sqrt[4]{81} = 3$

$h) \sqrt[3]{ \sqrt[4]{ {12}^{12} } } = \sqrt[3.4]{ {12}^{12} } = \sqrt[12]{ {12}^{12} } = {12}^{ \frac{12}{12} } = 12$

$i) \sqrt{ \sqrt[3]{ \sqrt[4]{ {3}^{48} } } } = \sqrt[2.3.4]{ {3}^{48} } = \sqrt[24]{ {3}^{48} } = {3}^{ \frac{48}{24} } = {3}^{2} = 9$

Espero ter ajudado.

Bons estudos.