Rešite ((23/9div3)^-2/94^2*frac{2/5})^-1

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

Ovrednoti

$$\frac{49}{40}=1,225$$

Koraki rešitve

Izrazite \frac{\frac{2\times 9+3}{9}}{3} kot enojni ulomek.

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

Pomnožite 2 in 9, da dobite 18.

$$\left(\frac{\left(\frac{18+3}{9\times 3}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \frac{2}{5}}\right)^{-1}$$

Seštejte 18 in 3, da dobite 21.

$$\left(\frac{\left(\frac{21}{9\times 3}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \frac{2}{5}}\right)^{-1}$$

Pomnožite 9 in 3, da dobite 27.

$$\left(\frac{\left(\frac{21}{27}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \frac{2}{5}}\right)^{-1}$$

Zmanjšajte ulomek \frac{21}{27} na najmanjši imenovalec tako, da izpeljete in okrajšate 3.

$$\left(\frac{\left(\frac{7}{9}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \frac{2}{5}}\right)^{-1}$$

Izračunajte potenco \frac{7}{9} števila -2, da dobite \frac{81}{49}.

$$\left(\frac{\frac{81}{49}}{\left(\frac{9}{4}\right)^{2}\times \frac{2}{5}}\right)^{-1}$$

Izračunajte potenco \frac{9}{4} števila 2, da dobite \frac{81}{16}.

$$\left(\frac{\frac{81}{49}}{\frac{81}{16}\times \frac{2}{5}}\right)^{-1}$$

Pomnožite \frac{81}{16} in \frac{2}{5}, da dobite \frac{81}{40}.

$$\left(\frac{\frac{81}{49}}{\frac{81}{40}}\right)^{-1}$$

Delite \frac{81}{49} s/z \frac{81}{40} tako, da pomnožite \frac{81}{49} z obratno vrednostjo \frac{81}{40}.

$$\left(\frac{81}{49}\times \frac{40}{81}\right)^{-1}$$

Pomnožite \frac{81}{49} in \frac{40}{81}, da dobite \frac{40}{49}.

$$\left(\frac{40}{49}\right)^{-1}$$

Izračunajte potenco \frac{40}{49} števila -1, da dobite \frac{49}{40}.

$$\frac{49}{40}$$

Faktoriziraj

$$\frac{7 ^ {2}}{2 ^ {3} \cdot 5} = 1\frac{9}{40} = 1,225$$