Question

Решите пожалуйста 3 И 4.СРОЧНО

Answer 1

$3)\sqrt[3]{\frac{27a^{5}}{b^{2}}}*\sqrt[3]{\frac{ab^{11}}{8}}=\sqrt[3]{\frac{3^{3}a^{5}*ab^{11}}{b^{2}*2^{3}}}=\sqrt[3]{\frac{3^{3}*(a^{2})^{3}*(b^{3})^{3}}{2^{3}}}=\frac{3a^{2}b^{3}}{2}=1,5a^{2} b^{3}\\\\Otvet:\boxed{1,5a^{2}b^{3}}$

$\sqrt[6]{\frac{m^{3}n^{4}}{192}}:\sqrt[6]{\frac{m^{15} }{3n^{8}}}=\sqrt[6]{\frac{m^{3}n^{4}*3n^{8}}{192m^{15}}}=\sqrt[6]{\frac{(n^{2})^{6}}{2^{6}*(m^{2})^{6}}}=\frac{n^{2}}{2m^{2}}\\\\Otvet:\boxed{\frac{n^{2}}{2m^{2}}}$

$4)\sqrt[4]{10-\sqrt{19}}*\sqrt[4]{10+\sqrt{19}}=\sqrt[4]{(10-\sqrt{19})(10+\sqrt{19})}=\sqrt[4]{10^{2}-(\sqrt{19})^{2}}=\sqrt[4]{100-19}=\sqrt[4]{81}=\sqrt[4]{3^{4}}=3\\\\Otvet.\boxed{3}$