Question

Alguém mim ajudar por favor urgente ser agora ​

Answer 1

Resposta:

$\sqrt[3x5]{ {10}^{5} } \times \sqrt[5 \times 3]{ {10}^{3} } = \\ \sqrt[15]{ {10}^{5} } \times \sqrt[15]{ {10}^{3} } = \sqrt[15]{ {10 }^{8} }$

$\sqrt{7} \div \sqrt[5]{7} = \\ \sqrt[2 \times 5]{ {7}^{5} } \div \sqrt[5 \times 2]{ {7}^{2} } = \\ \sqrt[10]{ {7}^{5} } \div \sqrt[10]{ {7}^{2} } = \\ {7}^{ \frac{5}{10} } \div {7}^{ \frac{2}{10} } = \\ {7}^{ \frac{5}{10} - \frac{2}{10} } = {7}^{ \frac{3}{10} } = \sqrt[10]{ {7}^{3} } = \sqrt[10]{343}$

$\sqrt[4 \times 2]{ {3}^{2} } \times \sqrt[2 \times 4]{ {3}^{4} } = \\ \sqrt[8]{ {3}^{2} } \times \sqrt[8]{ {3}^{4} } = \\ \sqrt[8]{ {3}^{6} } = \sqrt[4]{ {3}^{3} } = \sqrt[4]{27}$

$\sqrt[2 \times 10]{ {2}^{10} } \div \sqrt[20]{ {2}^{7} } = \\ \sqrt[20]{ {2}^{10} } \div \sqrt[20]{ {2}^{7} } = \\ \sqrt[20]{ {2}^{3} } = \sqrt[20]{8}$

$\sqrt[6]{ {5}^{2} } \div \sqrt[10]{ {5}^{3} } = \\ \sqrt[6 \times 5]{ {5}^{2 \times 5} } \div \sqrt[10 \times 3]{ {5}^{3 \times 3} } \\ \sqrt[30]{ {5}^{10} } \div \sqrt[30]{ {5}^{9} } = \\ \sqrt[30]{ {5}^{10 - 9} } = \sqrt[30]{5}$

$\sqrt[6]{ {7}^{5} } \div \sqrt[3 \times 2]{ {7}^{2 \times 2} } = \\ \sqrt[6]{ {7}^{5} } \div \sqrt[6]{ {7}^{4} } = \\ \sqrt[6]{ {7}^{5 - 4} } = \sqrt[6]{7}$