Основанонаупр.19стр.11.

Решиуравнение
\(x^3=125\) , \(x=\sqrt[3]{125}\) , \(x=\sqrt[3]{5^3}\) , \(x=5\) .

1. \(x^4=10000\) , \(x^4=\) [ \(\sqrt[4]{(\plusmn10)^4}\) | \(\sqrt[4]{(\plusmn100)^4}\) | \(\sqrt[4]{(\plusmn100)^3}\) ]; \(x=\) [ \(\plusmn10\) | \(\plusmn100\) | \(\plusmn1000\) ];

2. \(x^5=-\dfrac{1}{32}\) , \(x^5=\) [ \(\sqrt[4]{-\frac{1}{32}}\) | \(\sqrt[5]{\frac{1}{32}}\) | \(\sqrt[5]{-\frac{1}{32}}\) ] \(=\) [ \(\sqrt[5]{(-\frac{1}{2})^5}\) | \(\sqrt[5]{(\frac{1}{2})^5}\) | \(\sqrt[5]{(-\frac{1}{5})^2}\) ]; \(x=\) [ \(-\frac{1}{5}\) | \(-\frac{1}{2}\) | \(-\frac{1}{3}\) ];

3. \(x^4=-16\) , \(x=\) [ \(\sqrt[4]{-16}\) | \(\sqrt[4]{16}\) | \(\sqrt[4]{-4}\) ]; \(-16\) [ \(\gt 0\) | \(\lt 0\) ],следовательно,[есть корни|нет корней].