Question

Me ajudem ; com cálculos​

Answer 1

a)

$\sqrt[3]{8} \div \sqrt{2} = \sqrt[6]{ {8}^{2} } \div \sqrt[6]{ {2}^{3} } \\ = \sqrt[6]{ {8}^{2} \div {2}^{3} } = \sqrt[6]{ {2}^{6} \div {2}^{3} } = \sqrt[6]{ {2}^{3} } \\ = \sqrt{2}$

b)

$\sqrt[8]{16} \div \sqrt[12]{64} \\ = \sqrt[8]{ {2}^{4} } \div \sqrt[12]{ {2}^{6} } = \sqrt[24]{ {2}^{12} } \div \sqrt[24]{ {2}^{12} } \\ = 1$

c)

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

d)

$\sqrt[3]{10} \div \sqrt{2} = \sqrt[6]{ {10}^{2} } \div \sqrt[6]{ {2}^{3} } \\ = \sqrt[6]{100 \div 8} = \sqrt[6]{ \frac{100}{8} } e) [tex] \sqrt[5]{7} \div \sqrt[6]{7} = \sqrt[30]{ {7}^{6} } \div \sqrt[30]{ {7}^{5} } \\ = \sqrt[30]{ {7}^{6} \div {7}^{5} } = \sqrt[30]{7}$

f)

$\sqrt[4]{8} \div \sqrt[8]{8} = \sqrt[4]{ {2}^{3} } \div \sqrt[8]{ {2}^{3} } \\ = \sqrt[8]{ {2}^{6} } \div \sqrt[8]{ {2}^{3} } = \sqrt[8]{ {2}^{6} \div {2}^{3} } = \sqrt[8]{ {2}^{3} } \\ = \sqrt[8]{8}$