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

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

Evalwa

$$\frac{289}{40}=7.225$$

Passi tas-Soluzzjonijiet

Esprimi \frac{\frac{3}{9}}{3} bħala frazzjoni waħda.

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

Immultiplika 9 u 3 biex tikseb 27.

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

Naqqas il-frazzjoni \frac{3}{27} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 3.

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

Naqqas \frac{1}{9} minn 2 biex tikseb \frac{17}{9}.

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

Ikkalkula \frac{17}{9} bil-power ta' -2 u tikseb \frac{81}{289}.

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

Ikkalkula \frac{9}{4} bil-power ta' 2 u tikseb \frac{81}{16}.

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

Immultiplika \frac{81}{16} u \frac{2}{5} biex tikseb \frac{81}{40}.

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

Iddividi \frac{81}{289} b'\frac{81}{40} billi timmultiplika \frac{81}{289} bir-reċiproku ta' \frac{81}{40}.

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

Immultiplika \frac{81}{289} u \frac{40}{81} biex tikseb \frac{40}{289}.

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

Ikkalkula \frac{40}{289} bil-power ta' -1 u tikseb \frac{289}{40}.

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

Fattur

$$\frac{17 ^ {2}}{2 ^ {3} \cdot 5} = 7\frac{9}{40} = 7.225$$