Réitigh {[(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

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

Luacháil

$$25$$

Céimeanna Réitigh

Roinn 2 faoi 2 chun 1 a fháil.

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

Dealaigh \frac{3}{8} ó 1 chun \frac{5}{8} a fháil.

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

Suimigh \frac{5}{8} agus \frac{4}{5} chun \frac{57}{40} a fháil.

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

Dealaigh \frac{11}{20} ó \frac{57}{40} chun \frac{7}{8} a fháil.

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

Suimigh \frac{3}{14} agus \frac{5}{7} chun \frac{13}{14} a fháil.

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

Dealaigh 1 ó \frac{13}{14} chun -\frac{1}{14} a fháil.

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

Suimigh -\frac{1}{14} agus \frac{3}{2} chun \frac{10}{7} a fháil.

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

Méadaigh \frac{7}{8} agus \frac{10}{7} chun \frac{5}{4} a fháil.

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

Ríomh cumhacht \frac{5}{4} de 2 agus faigh \frac{25}{16}.

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

Laghdaigh an codán \frac{2}{4} chuig na téarmaí is ísle trí 2 a bhaint agus a chealú.

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

Suimigh -1 agus \frac{1}{2} chun -\frac{1}{2} a fháil.

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

Ríomh cumhacht -\frac{1}{2} de 2 agus faigh \frac{1}{4}.

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

Roinn \frac{25}{16} faoi \frac{1}{4} trí \frac{25}{16} a mhéadú faoi dheilín \frac{1}{4}.

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

Méadaigh \frac{25}{16} agus 4 chun \frac{25}{4} a fháil.

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

Ríomh cumhacht \frac{25}{4} de 2 agus faigh \frac{625}{16}.

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

Suimigh \frac{5}{6} agus \frac{1}{2} chun \frac{4}{3} a fháil.

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

Dealaigh \frac{1}{12} ó \frac{4}{3} chun \frac{5}{4} a fháil.

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

Ríomh cumhacht \frac{5}{4} de 2 agus faigh \frac{25}{16}.

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

Roinn \frac{625}{16} faoi \frac{25}{16} trí \frac{625}{16} a mhéadú faoi dheilín \frac{25}{16}.

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

Méadaigh \frac{625}{16} agus \frac{16}{25} chun 25 a fháil.

$$25$$

Fachtóirigh

$$5^{2}$$