Doprowadź do najprostszej ...- Zadanie 3: Matematyka 1. Zakres rozszerzony. Cześć 1

Rozwiązanie

Upraszczamy wyrażenie.

$3 x^{3} \cdot 3 x^{4} : 6 x^{5} \cdot 4 x^{2} : 3 x^{2} = 3 (x^{3})^{\frac{1}{2}} \cdot (x^{4})^{\frac{1}{3}} : (x^{5})^{\frac{1}{6}} \cdot 4 x^{2} : (x^{2})^{\frac{1}{3}} =$

$= 3 x^{3 \cdot \frac{1}{2}} \cdot x^{4 \cdot \frac{1}{3}} : x^{5 \cdot \frac{1}{6}} \cdot 4 x^{2} : x^{2 \cdot \frac{1}{3}} = 3 x^{\frac{3}{2}} \cdot x^{\frac{4}{3}} : x^{\frac{5}{6}} \cdot 4 x^{2} : x^{\frac{2}{3}} =$

$= 3 x^{\frac{18}{12}} \cdot x^{\frac{16}{12}} : x^{\frac{10}{12}} \cdot 4 x^{\frac{6}{3}} : x^{\frac{2}{3}} = 3 x^{\frac{18}{12} + \frac{16}{12} - \frac{10}{12}} \cdot 4 x^{\frac{6}{3} - \frac{2}{3}} = 3 x^{\frac{24}{12}} \cdot 4 x^{\frac{4}{3}} =$

$= 3 x^{2} \cdot 4 x^{\frac{4}{3}} = (x^{2})^{\frac{1}{3}} \cdot (x^{\frac{4}{3}})^{\frac{1}{4}} = x^{\frac{2}{3}} \cdot x^{\frac{4}{3} \cdot \frac{1}{4}} = x^{\frac{2}{3}} \cdot x^{\frac{1}{3}} = x^{\frac{2}{3} + \frac{1}{3}} = x^{1} = x$