Ratkaise {[(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

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

Laske

$$25$$

Ratkaisun vaiheet

Jaa 2 luvulla 2, jolloin ratkaisuksi tulee 1.

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

Vähennä \frac{3}{8} luvusta 1 saadaksesi tuloksen \frac{5}{8}.

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

Selvitä \frac{57}{40} laskemalla yhteen \frac{5}{8} ja \frac{4}{5}.

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

Vähennä \frac{11}{20} luvusta \frac{57}{40} saadaksesi tuloksen \frac{7}{8}.

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

Selvitä \frac{13}{14} laskemalla yhteen \frac{3}{14} ja \frac{5}{7}.

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

Vähennä 1 luvusta \frac{13}{14} saadaksesi tuloksen -\frac{1}{14}.

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

Selvitä \frac{10}{7} laskemalla yhteen -\frac{1}{14} ja \frac{3}{2}.

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

Kerro \frac{7}{8} ja \frac{10}{7}, niin saadaan \frac{5}{4}.

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

Laske \frac{5}{4} potenssiin 2, jolloin ratkaisuksi tulee \frac{25}{16}.

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

Supista murtoluku \frac{2}{4} luvulla 2.

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

Selvitä -\frac{1}{2} laskemalla yhteen -1 ja \frac{1}{2}.

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

Laske -\frac{1}{2} potenssiin 2, jolloin ratkaisuksi tulee \frac{1}{4}.

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

Jaa \frac{25}{16} luvulla \frac{1}{4} kertomalla \frac{25}{16} luvun \frac{1}{4} käänteisluvulla.

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

Kerro \frac{25}{16} ja 4, niin saadaan \frac{25}{4}.

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

Laske \frac{25}{4} potenssiin 2, jolloin ratkaisuksi tulee \frac{625}{16}.

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

Selvitä \frac{4}{3} laskemalla yhteen \frac{5}{6} ja \frac{1}{2}.

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

Vähennä \frac{1}{12} luvusta \frac{4}{3} saadaksesi tuloksen \frac{5}{4}.

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

Laske \frac{5}{4} potenssiin 2, jolloin ratkaisuksi tulee \frac{25}{16}.

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

Jaa \frac{625}{16} luvulla \frac{25}{16} kertomalla \frac{625}{16} luvun \frac{25}{16} käänteisluvulla.

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

Kerro \frac{625}{16} ja \frac{16}{25}, niin saadaan 25.

$$25$$

Jaa tekijöihin

$$5^{2}$$