Question

Пожалуйста помогите с корнями

Answer 1

Объяснение:

107.

$1)\ \sqrt[3]{10^6}=10^{\frac{6}{3}}=10^2=100.\\2)\ \sqrt[3]{3^{12}} =3^\frac{12}{3} =3^4=81.\\3)\ \sqrt[4]{(\frac{1}{2})^{12}} } =(\frac{1}{2})^{\frac{12}{4} } =(\frac{1}{2})^3=\frac{1}{8}.\\4)\ \sqrt[4]{(\frac{1}{3})^{16} }=(\frac{1}{3})^{\frac{16}{4}}=(\frac{1}{3})^4=\frac{1}{81}.\\5)\ \sqrt[5]{32^2} =\sqrt[5]{(2^5)^2}=\sqrt[5]{2^{10}}=2^{\frac{10}{5}}=2^2=4.$

Answer 2

$1) \ \sqrt[3]{10^{6} } =\sqrt[3]{(10^{2} )^{3} } =10^{2} =\boxed{100}\\\\\\2) \ \sqrt[3]{3^{12} } =\sqrt[3]{(3^{4})^{3} } =3^{4} =\boxed{81}\\\\\\3) \ \sqrt[4]{\Big(\dfrac{1}{2} \Big)^{12} } =\sqrt[4]{\Big[\Big(\dfrac{1}{2} \Big)^{3} \Big]^{4} } =\Big(\dfrac{1}{2}\Big)^{3} =\dfrac{1}{8}= \boxed{0,125}$

$4) \ \sqrt[4]{\Big(\dfrac{1}{3} \Big)^{16} } =\sqrt[4]{\Big[\Big(\dfrac{1}{3} \Big)^{4} \Big]^{4} } =\Big(\dfrac{1}{3}\Big)^{4} =\boxed{\dfrac{1}{81} }\\\\\\5) \ \sqrt[5]{32^{2} } =\sqrt[5]{(2^{5} )^{2} } =\sqrt[5]{(2^{2} )^{5} } =2^{2} =\boxed4$