1166. a) \(\frac{2}{3a}\) \(\sqrt{72a^3b}\); б) \(\frac{x^2}{b}\) \(\sqrt[3]{\frac{72a^3b^3}{343x^3}}\); в) \(\frac{3}{x}\) \(\sqrt{\frac{a^5x^2}{18}}\); г) 3mn \(\sqrt[4]{\frac{80x^3}{243m^7n^5}}\).

Краткое пояснение:

Пошаговое решение:

1. a) \(\frac{2}{3a}\) \(\sqrt{72a^3b}\)
   \(\frac{2}{3a}\) \(\sqrt{36a^2 · 2ab}\) = \(\frac{2}{3a}\) \(6a\) \(\sqrt{2ab}\) = 4\(\sqrt{2ab}\).
2. б) \(\frac{x^2}{b}\) \(\sqrt[3]{\frac{72a^3b^3}{343x^3}}\)
   \(\frac{x^2}{b}\) \(\frac{\sqrt[3]{72a^3b^3}}{\sqrt[3]{343x^3}}\) = \(\frac{x^2}{b}\) \(\frac{a b \sqrt[3]{72}}{7x}\) = \(\frac{x^2}{b}\) \(\frac{a b \sqrt[3]{8 · 9}}{7x}\) = \(\frac{x^2}{b}\) \(\frac{a b \cdot 2 \sqrt[3]{9}}{7x}\) = \(\frac{2ax · \sqrt[3]{9}}{7}\).
3. в) \(\frac{3}{x}\) \(\sqrt{\frac{a^5x^2}{18}}\)
   \(\frac{3}{x}\) \(\sqrt{\frac{a^4x^2 · a}{18}}\) = \(\frac{3}{x}\) \(ax\) \(\sqrt{\frac{a}{18}}\) = 3a \(\sqrt{\frac{a}{18}}\)
   = 3a \(\sqrt{\frac{a · 2}{18 · 2}}\)= 3a \(\sqrt{\frac{2a}{36}}\)= 3a \(\frac{\sqrt{2a}}{6}\) = \(\frac{a \sqrt{2a}}{2}\).
4. г) 3mn \(\sqrt[4]{\frac{80x^3}{243m^7n^5}}\)
   3mn \(\sqrt[4]{\frac{16 · 5 x^3}{81 m^4 n^4 · 3m n}}\)
   = 3mn \(\frac{2}{3mn}\) \(\sqrt[4]{\frac{5x^3}{3mn}}\)
   = 2 \(\sqrt[4]{\frac{5x^3}{3mn}}\).

Ответ: a) 4√(2ab); б) \(\frac{2ax \sqrt[3]{9}}{7}\); в) \(\frac{a \sqrt{2a}}{2}\); г) 2 \(\sqrt[4]{\frac{5x^3}{3mn}}\).