Question

Preciso pra hoje, alguém me ajuda por favor
Potência fracionária ​

Answer 1

Resposta:

1) S = { 4 ; 243 }

2) S = { 25 ; $\sqrt{10}$ }

3) S = { $2^{\frac{1}{2} }$ ; $5^{\frac{3}{2} }$ ; $13^{\frac{7}{5} }$ }

4) S = { $\sqrt[2]{3}$ ; $\sqrt[7]{15^{2} }$ ; $\sqrt[3]{111^{2} }$ }

5) S = { 9 }

Explicação passo-a-passo:

1)

$64^{\frac{1}{3}} = \sqrt[3]{64^{1}} = 4\\\\81^{\frac{5}{4} } = \sqrt[4]{81^{5}} = \sqrt[4]{81^{4}\times81^{1}} = 81\sqrt[4]{81} = 81\times3 = 243$

2)

$\sqrt{5^{4}} = \sqrt{5^{2}\times5^{2}} = 5\times5 = 25\\\\\sqrt[6]{10^{3}} = 10^{\frac{3}{6}\div\frac{3}{3}} = 10^{\frac{1}{2}} = \sqrt{10}$

3)

$\sqrt[2]{2} = 2^{\frac{1}{2} } \\\\\sqrt[2]{5^{3}} = 5^{\frac{3}{2}}\\\\\sqrt[5]{13^{7}} = 13^{\frac{7}{5} }$

4)

$3^{\frac{1}{2} } = \sqrt[2]{3} \\\\15^{\frac{2}{7} } = \sqrt[7]{15^{2}} \\\\111^{\frac{2}{3} } = \sqrt[3]{111^{2}}$

5)

$3^{\frac{1}{2} } \times 3^{\frac{3}{2} } = 3^{\frac{1}{2}+\frac{3}{2} } = 3^{\frac{4}{2}} = 3^{2} = 9$