\(\sqrt{ \frac{9x^{4}a^{5}} {b^{3}} } : \frac{3 x^{2} \cdot \sqrt{\frac{a}{b}}}{a^{-2} b} \)
\(= \frac{3x^{2}a^{2,5}} {b^{1,5}} : \frac{3 x^{2} \cdot a^{0,5}{b^{-0,5}}}{a^{-2} b} \)
\(= \frac{3x^{2}a^{2,5}} {b^{1,5}} \cdot \frac{a^{-2} b} {3 x^{2} \cdot a^{0,5}{b^{-0,5}}}\)
3x^2 kürzen
\(= \frac{a^{2,5}} {b^{1,5}} \cdot \frac{a^{-2} b} { a^{0,5}{b^{-0,5}}}\)
\(= \frac{a^{0,5} b} { a^{0,5}{b}} = 1 \)