Atrisiniet {(1+3/4-1/2)^2:[1-(5/4-1/2)]^2*(frac{2}{5}:frac{5}{4})*frac{1}{14}}^2

$$\{ ( 1 + \frac { 3 } { 4 } - \frac { 1 } { 2 } ) ^ { 2 } : [ 1 - ( \frac { 5 } { 4 } - \frac { 1 } { 2 } ) ] ^ { 2 } \cdot ( \frac { 2 } { 5 } : \frac { 5 } { 4 } ) \cdot \frac { 1 } { 14 } \} ^ { 2 }$$

Izrēķināt

$$\frac{16}{49}\approx 0,326530612$$

Atrisinājuma darbības

Saskaitiet 1 un \frac{3}{4}, lai iegūtu \frac{7}{4}.

$$\left(\frac{\left(\frac{7}{4}-\frac{1}{2}\right)^{2}}{\left(1-\left(\frac{5}{4}-\frac{1}{2}\right)\right)^{2}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\right)^{2}$$

Atņemiet \frac{1}{2} no \frac{7}{4}, lai iegūtu \frac{5}{4}.

$$\left(\frac{\left(\frac{5}{4}\right)^{2}}{\left(1-\left(\frac{5}{4}-\frac{1}{2}\right)\right)^{2}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\right)^{2}$$

Aprēķiniet \frac{5}{4} pakāpē 2 un iegūstiet \frac{25}{16}.

$$\left(\frac{\frac{25}{16}}{\left(1-\left(\frac{5}{4}-\frac{1}{2}\right)\right)^{2}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\right)^{2}$$

Atņemiet \frac{1}{2} no \frac{5}{4}, lai iegūtu \frac{3}{4}.

$$\left(\frac{\frac{25}{16}}{\left(1-\frac{3}{4}\right)^{2}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\right)^{2}$$

Atņemiet \frac{3}{4} no 1, lai iegūtu \frac{1}{4}.

$$\left(\frac{\frac{25}{16}}{\left(\frac{1}{4}\right)^{2}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\right)^{2}$$

Aprēķiniet \frac{1}{4} pakāpē 2 un iegūstiet \frac{1}{16}.

$$\left(\frac{\frac{25}{16}}{\frac{1}{16}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\right)^{2}$$

Daliet \frac{25}{16} ar \frac{1}{16}, reizinot \frac{25}{16} ar apgriezto daļskaitli \frac{1}{16} .

$$\left(\frac{25}{16}\times 16\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\right)^{2}$$

Reiziniet \frac{25}{16} un 16, lai iegūtu 25.

$$\left(25\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\right)^{2}$$

Daliet \frac{2}{5} ar \frac{5}{4}, reizinot \frac{2}{5} ar apgriezto daļskaitli \frac{5}{4} .

$$\left(25\times \frac{2}{5}\times \frac{4}{5}\times \frac{1}{14}\right)^{2}$$

Reiziniet \frac{2}{5} un \frac{4}{5}, lai iegūtu \frac{8}{25}.

$$\left(25\times \frac{8}{25}\times \frac{1}{14}\right)^{2}$$

Reiziniet 25 un \frac{8}{25}, lai iegūtu 8.

$$\left(8\times \frac{1}{14}\right)^{2}$$

Reiziniet 8 un \frac{1}{14}, lai iegūtu \frac{4}{7}.

$$\left(\frac{4}{7}\right)^{2}$$

Aprēķiniet \frac{4}{7} pakāpē 2 un iegūstiet \frac{16}{49}.

$$\frac{16}{49}$$

Sadalīt reizinātājos

$$\frac{2 ^ {4}}{7 ^ {2}} = 0,32653061224489793$$