Atrisiniet ((2-3/9div3)^-2/94^2*frac{2/5})^-1

$$( \frac { ( 2 - \frac { 3 } { 9 } \div 3 ) ^ { - 2 } } { \frac { 9 } { 4 } ^ { 2 } \cdot \frac { 2 } { 5 } } ) ^ { - 1 }$$

Izrēķināt

$$\frac{289}{40}=7,225$$

Atrisinājuma darbības

Izsakiet \frac{\frac{3}{9}}{3} kā vienu daļskaitli.

$$\left(\frac{\left(2-\frac{3}{9\times 3}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \frac{2}{5}}\right)^{-1}$$

Reiziniet 9 un 3, lai iegūtu 27.

$$\left(\frac{\left(2-\frac{3}{27}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \frac{2}{5}}\right)^{-1}$$

Vienādot daļskaitli \frac{3}{27} līdz mazākajam loceklim, izvelkot un saīsinot 3.

$$\left(\frac{\left(2-\frac{1}{9}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \frac{2}{5}}\right)^{-1}$$

Atņemiet \frac{1}{9} no 2, lai iegūtu \frac{17}{9}.

$$\left(\frac{\left(\frac{17}{9}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \frac{2}{5}}\right)^{-1}$$

Aprēķiniet \frac{17}{9} pakāpē -2 un iegūstiet \frac{81}{289}.

$$\left(\frac{\frac{81}{289}}{\left(\frac{9}{4}\right)^{2}\times \frac{2}{5}}\right)^{-1}$$

Aprēķiniet \frac{9}{4} pakāpē 2 un iegūstiet \frac{81}{16}.

$$\left(\frac{\frac{81}{289}}{\frac{81}{16}\times \frac{2}{5}}\right)^{-1}$$

Reiziniet \frac{81}{16} un \frac{2}{5}, lai iegūtu \frac{81}{40}.

$$\left(\frac{\frac{81}{289}}{\frac{81}{40}}\right)^{-1}$$

Daliet \frac{81}{289} ar \frac{81}{40}, reizinot \frac{81}{289} ar apgriezto daļskaitli \frac{81}{40} .

$$\left(\frac{81}{289}\times \frac{40}{81}\right)^{-1}$$

Reiziniet \frac{81}{289} un \frac{40}{81}, lai iegūtu \frac{40}{289}.

$$\left(\frac{40}{289}\right)^{-1}$$

Aprēķiniet \frac{40}{289} pakāpē -1 un iegūstiet \frac{289}{40}.

$$\frac{289}{40}$$

Sadalīt reizinātājos

$$\frac{17 ^ {2}}{2 ^ {3} \cdot 5} = 7\frac{9}{40} = 7,225$$