Question

Alguém pode me ajudar?? Quanto da essa conta?

Answer 1

Resposta:

$\sqrt[3]{25^{7}}=\sqrt[3]{(5^{2})^{7}}=\sqrt[3]{5^{14}}=5^{\frac{14}{3}}=5^{\frac{12}{3}}.5^{\frac{2}{3}}=5^{4}.5^{\frac{2}{3}}=625\sqrt[3]{5^{2}}=625\sqrt[3]{25}$

Propriedades:

$(a^{m})^{n}=a^{m.n}\\\\\sqrt[n]{x^m} =x^{\frac{m}{n} }\\\\a^{m}a^{n}=a^{m+n}\\\\\frac{a^{m}}{a^{n}}=a^{m-n} \\\\a^{0}=1\\\\a^{1}=a$