Question

Вычислите! "Корни n-ой степени из числа"

Answer 1

$1)\sqrt[4]{27}*\sqrt[4]{3}=\sqrt[4]{27*3}=\sqrt[4]{3^{3}*3 }=\sqrt[4]{3^{4}}=3\\\\Otvet:\boxed{3}\\\\2)\sqrt[3]{\frac{256}{625}}:\sqrt[3]{\frac{4}{5}}=\sqrt[3]{\frac{256}{625}*\frac{5}{4}}=\sqrt[3]{\frac{64}{125}}=\sqrt[3]{\frac{4^{3}}{5^{3}}}=\frac{4}{5}=0,8\\\\Otvet:\boxed{0,8}\\\\3)\sqrt[7]{5^{21}}=\sqrt[7]{(5^{3})^{7}}=5^{3}=125\\\\Otvet:\boxed{125}$

$4)\sqrt[3]{\sqrt[4]{4096}}=\sqrt[12]{4096}=\sqrt[12]{2^{12}}=2\\\\Otvet:\boxed{2}$

Answer 2

а)

$\sqrt[4]{27} *\sqrt[4]{3} =\sqrt[4]{27*3} =\sqrt[4]{3^{3}*3}=\sqrt[4]{3^{4}} =3$

б)

$\sqrt[3]{\frac{256}{652}}:\sqrt[3]{\frac{4}{5}}=\sqrt[3]{\frac{4^{4} }{5^{4} } } </strong><strong>:</strong><strong>\sqrt[3]{\frac{</strong><strong>4</strong><strong>}{</strong><strong>5</strong><strong>} } =\sqrt[3]{\frac{4^{3}*4}{5^{3}*5}} </strong><strong>:</strong><strong>\sqrt[3]{\frac{</strong><strong>4</strong><strong>}{</strong><strong>5</strong><strong>} } =\frac{4}{5}\sqrt[3]{\frac{</strong><strong>4</strong><strong>}{</strong><strong>5</strong><strong>} }:\sqrt[3]{\frac{</strong><strong>4</strong><strong>}{</strong><strong>5</strong><strong>} } =\frac{4}{5}=0,8$

в)

$\sqrt[7]{5^{21} } =\sqrt[7]{(5^{3})^{7}}=5^{3} =125$

г)

$\sqrt[3]{\sqrt[4]{4096} } =\sqrt[3*4]{4096} =\sqrt[12]{4096} =\sqrt[12]{2^{12} }=2$