Question

С! 100
фото в закрепе. хоть что нибудь решите

Answer 1

$4.5)3^{\frac{2}{3}} =\sqrt[3]{3^{2}}=\sqrt[3]{9}\\\\4^{\frac{3}{5}}=\sqrt[5]{4^{3}}=\sqrt[5]{64}\\\\6^{\frac{2}{3}}=\sqrt[3]{6^{2}}=\sqrt[3]{36}\\\\7^{\frac{5}{9}}=\sqrt[9]{7^{5}}=\sqrt[9]{16807}\\\\10^{0,6}=10^{\frac{3}{5}}=\sqrt[5]{10^{3}}=\sqrt[5]{1000}\\\\a^{1\frac{2}{3}}=a^{\frac{5}{3}}=\sqrt[3]{a^{5}} \\\\c^{1,4}=c^{\frac{7}{5}}=\sqrt[5]{c^{7}}\\\\x^{\frac{1}{n}}=\sqrt[n]{x}\\\\x^{\frac{n}{2}}=\sqrt{x^{n}}$

$4.7)25^{\frac{1}{2}}=\sqrt{25}=\sqrt{5^{2}}= 5\\\\49^{\frac{1}{2}}=\sqrt{49}=\sqrt{7^{2}}=7\\\\27^{\frac{1}{3}}=\sqrt[3]{27}=\sqrt[3]{3^{3}}=3\\\\16^{0,25}=16^{\frac{1}{4}}=\sqrt[4]{16}=\sqrt[4]{2^{4}}=2\\\\100^{0,5}=100^{\frac{1}{2}}=\sqrt{100}=\sqrt{10^{2}}=10\\\\16^{\frac{3}{4}}=\sqrt[4]{16^{3}}=\sqrt[4]{(2^{4} )^{3}}=\sqrt[4]{(2^{3})^{4}}=2^{3}=8\\\\27^{\frac{2}{3}}=\sqrt[3]{27^{2}} =\sqrt[3]{(3^{3})^{2}}=\sqrt[3]{(2^{2})^{3}}=2^{2}=4$

$25^{2,5}=25^{\frac{5}{2}}=\sqrt{25^{5}}=\sqrt{(25^{2})^{2}*5^{2}}=25^{2}*5=625*5=3125\\\\8^{\frac{5}{3}}=\sqrt[3]{8^{5}}=\sqrt[3]{(2^{3})^{5}}=\sqrt[3]{(2^{5})^{3}}=2^{5}=32\\\\27^{\frac{4}{3}}=\sqrt[3]{27^{4}}=\sqrt[3]{(3^{3})^{4}}=\sqrt[3]{(3^{4})^{3}=3^{4}}=81$