Riješi {[(1-3/8+4/5-11/20)*(3/14+frac{5}{7}-1+frac{3}{2})]^2:(-frac{2}{2}+frac{2}{4})^2}^2:(frac{5}{6}+frac{1}{2}-frac{1}{12})^2

$$\{ [ ( 1 - \frac { 3 } { 8 } + \frac { 4 } { 5 } - \frac { 11 } { 20 } ) \cdot ( \frac { 3 } { 14 } + \frac { 5 } { 7 } - 1 + \frac { 3 } { 2 } ) ] ^ { 2 } : ( - \frac { 2 } { 2 } + \frac { 2 } { 4 } ) ^ { 2 } \} ^ { 2 } : ( \frac { 5 } { 6 } + \frac { 1 } { 2 } - \frac { 1 } { 12 } ) ^ { 2 }$$

Izračunaj

$$25$$

Koraci rješenja

Podijelite 2 s 2 da biste dobili 1.

$$\frac{\left(\frac{\left(\left(1-\frac{3}{8}+\frac{4}{5}-\frac{11}{20}\right)\left(\frac{3}{14}+\frac{5}{7}-1+\frac{3}{2}\right)\right)^{2}}{\left(-1+\frac{2}{4}\right)^{2}}\right)^{2}}{\left(\frac{5}{6}+\frac{1}{2}-\frac{1}{12}\right)^{2}}$$

Oduzmite \frac{3}{8} od 1 da biste dobili \frac{5}{8}.

$$\frac{\left(\frac{\left(\left(\frac{5}{8}+\frac{4}{5}-\frac{11}{20}\right)\left(\frac{3}{14}+\frac{5}{7}-1+\frac{3}{2}\right)\right)^{2}}{\left(-1+\frac{2}{4}\right)^{2}}\right)^{2}}{\left(\frac{5}{6}+\frac{1}{2}-\frac{1}{12}\right)^{2}}$$

Dodajte \frac{5}{8} broju \frac{4}{5} da biste dobili \frac{57}{40}.

$$\frac{\left(\frac{\left(\left(\frac{57}{40}-\frac{11}{20}\right)\left(\frac{3}{14}+\frac{5}{7}-1+\frac{3}{2}\right)\right)^{2}}{\left(-1+\frac{2}{4}\right)^{2}}\right)^{2}}{\left(\frac{5}{6}+\frac{1}{2}-\frac{1}{12}\right)^{2}}$$

Oduzmite \frac{11}{20} od \frac{57}{40} da biste dobili \frac{7}{8}.

$$\frac{\left(\frac{\left(\frac{7}{8}\left(\frac{3}{14}+\frac{5}{7}-1+\frac{3}{2}\right)\right)^{2}}{\left(-1+\frac{2}{4}\right)^{2}}\right)^{2}}{\left(\frac{5}{6}+\frac{1}{2}-\frac{1}{12}\right)^{2}}$$

Dodajte \frac{3}{14} broju \frac{5}{7} da biste dobili \frac{13}{14}.

$$\frac{\left(\frac{\left(\frac{7}{8}\left(\frac{13}{14}-1+\frac{3}{2}\right)\right)^{2}}{\left(-1+\frac{2}{4}\right)^{2}}\right)^{2}}{\left(\frac{5}{6}+\frac{1}{2}-\frac{1}{12}\right)^{2}}$$

Oduzmite 1 od \frac{13}{14} da biste dobili -\frac{1}{14}.

$$\frac{\left(\frac{\left(\frac{7}{8}\left(-\frac{1}{14}+\frac{3}{2}\right)\right)^{2}}{\left(-1+\frac{2}{4}\right)^{2}}\right)^{2}}{\left(\frac{5}{6}+\frac{1}{2}-\frac{1}{12}\right)^{2}}$$

Dodajte -\frac{1}{14} broju \frac{3}{2} da biste dobili \frac{10}{7}.

$$\frac{\left(\frac{\left(\frac{7}{8}\times \frac{10}{7}\right)^{2}}{\left(-1+\frac{2}{4}\right)^{2}}\right)^{2}}{\left(\frac{5}{6}+\frac{1}{2}-\frac{1}{12}\right)^{2}}$$

Pomnožite \frac{7}{8} i \frac{10}{7} da biste dobili \frac{5}{4}.

$$\frac{\left(\frac{\left(\frac{5}{4}\right)^{2}}{\left(-1+\frac{2}{4}\right)^{2}}\right)^{2}}{\left(\frac{5}{6}+\frac{1}{2}-\frac{1}{12}\right)^{2}}$$

Izračunajte koliko je 2 na \frac{5}{4} da biste dobili \frac{25}{16}.

$$\frac{\left(\frac{\frac{25}{16}}{\left(-1+\frac{2}{4}\right)^{2}}\right)^{2}}{\left(\frac{5}{6}+\frac{1}{2}-\frac{1}{12}\right)^{2}}$$

Skratite razlomak \frac{2}{4} na najmanje vrijednosti tako da izlučite i poništite 2.

$$\frac{\left(\frac{\frac{25}{16}}{\left(-1+\frac{1}{2}\right)^{2}}\right)^{2}}{\left(\frac{5}{6}+\frac{1}{2}-\frac{1}{12}\right)^{2}}$$

Dodajte -1 broju \frac{1}{2} da biste dobili -\frac{1}{2}.

$$\frac{\left(\frac{\frac{25}{16}}{\left(-\frac{1}{2}\right)^{2}}\right)^{2}}{\left(\frac{5}{6}+\frac{1}{2}-\frac{1}{12}\right)^{2}}$$

Izračunajte koliko je 2 na -\frac{1}{2} da biste dobili \frac{1}{4}.

$$\frac{\left(\frac{\frac{25}{16}}{\frac{1}{4}}\right)^{2}}{\left(\frac{5}{6}+\frac{1}{2}-\frac{1}{12}\right)^{2}}$$

Podijelite \frac{25}{16} s \frac{1}{4} tako da pomnožite \frac{25}{16} s brojem recipročnim broju \frac{1}{4}.

$$\frac{\left(\frac{25}{16}\times 4\right)^{2}}{\left(\frac{5}{6}+\frac{1}{2}-\frac{1}{12}\right)^{2}}$$

Pomnožite \frac{25}{16} i 4 da biste dobili \frac{25}{4}.

$$\frac{\left(\frac{25}{4}\right)^{2}}{\left(\frac{5}{6}+\frac{1}{2}-\frac{1}{12}\right)^{2}}$$

Izračunajte koliko je 2 na \frac{25}{4} da biste dobili \frac{625}{16}.

$$\frac{\frac{625}{16}}{\left(\frac{5}{6}+\frac{1}{2}-\frac{1}{12}\right)^{2}}$$

Dodajte \frac{5}{6} broju \frac{1}{2} da biste dobili \frac{4}{3}.

$$\frac{\frac{625}{16}}{\left(\frac{4}{3}-\frac{1}{12}\right)^{2}}$$

Oduzmite \frac{1}{12} od \frac{4}{3} da biste dobili \frac{5}{4}.

$$\frac{\frac{625}{16}}{\left(\frac{5}{4}\right)^{2}}$$

Izračunajte koliko je 2 na \frac{5}{4} da biste dobili \frac{25}{16}.

$$\frac{\frac{625}{16}}{\frac{25}{16}}$$

Podijelite \frac{625}{16} s \frac{25}{16} tako da pomnožite \frac{625}{16} s brojem recipročnim broju \frac{25}{16}.

$$\frac{625}{16}\times \frac{16}{25}$$

Pomnožite \frac{625}{16} i \frac{16}{25} da biste dobili 25.

$$25$$

Faktor

$$5^{2}$$