Riješi ((2*3/9div3)^-2/(frac{9{4})^2*(2/5)^-1})^-1

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

Procijeni

$$\frac{5}{8}=0,625$$

Koraci za rješenje

Svedite razlomak \frac{3}{9} na najprostije elemente rastavlјanjem i kraćenjem 3.

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

Pomnožite 2 i \frac{1}{3} da biste dobili \frac{2}{3}.

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

Izrazite \frac{\frac{2}{3}}{3} kao jedan razlomak.

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

Pomnožite 3 i 3 da biste dobili 9.

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

Izračunajte \frac{2}{9} stepen od -2 i dobijte \frac{81}{4}.

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

Izračunajte \frac{9}{4} stepen od 2 i dobijte \frac{81}{16}.

$$\left(\frac{\frac{81}{4}}{\frac{81}{16}\times \left(\frac{2}{5}\right)^{-1}}\right)^{-1}$$

Izračunajte \frac{2}{5} stepen od -1 i dobijte \frac{5}{2}.

$$\left(\frac{\frac{81}{4}}{\frac{81}{16}\times \frac{5}{2}}\right)^{-1}$$

Pomnožite \frac{81}{16} i \frac{5}{2} da biste dobili \frac{405}{32}.

$$\left(\frac{\frac{81}{4}}{\frac{405}{32}}\right)^{-1}$$

Podijelite \frac{81}{4} sa \frac{405}{32} tako što ćete pomnožiti \frac{81}{4} recipročnom vrijednošću od \frac{405}{32}.

$$\left(\frac{81}{4}\times \frac{32}{405}\right)^{-1}$$

Pomnožite \frac{81}{4} i \frac{32}{405} da biste dobili \frac{8}{5}.

$$\left(\frac{8}{5}\right)^{-1}$$

Izračunajte \frac{8}{5} stepen od -1 i dobijte \frac{5}{8}.

$$\frac{5}{8}$$

Faktor

$$\frac{5}{2 ^ {3}} = 0,625$$