Lahenda {left({left(2-frac{3/9/3right)}^-2}{{left(9/4right)}^22^-1/5}right)}^-1

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

Arvuta

$$\frac{289}{160}=1,80625$$

Lahenduse etapid

Avaldage \frac{\frac{3}{9}}{3} ühe murdarvuna.

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

Korrutage 9 ja 3, et leida 27.

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

Taandage murd \frac{3}{27} vähimale ühiskordsele, eraldades ja taandades arvu 3.

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

Lahutage \frac{1}{9} väärtusest 2, et leida \frac{17}{9}.

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

Arvutage -2 aste \frac{17}{9} ja leidke \frac{81}{289}.

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

Arvutage 2 aste \frac{9}{4} ja leidke \frac{81}{16}.

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

Arvutage -1 aste 2 ja leidke \frac{1}{2}.

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

Avaldage \frac{\frac{1}{2}}{5} ühe murdarvuna.

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

Korrutage 2 ja 5, et leida 10.

$$\left(\frac{\frac{81}{289}}{\frac{81}{16}\times \frac{1}{10}}\right)^{-1}$$

Korrutage \frac{81}{16} ja \frac{1}{10}, et leida \frac{81}{160}.

$$\left(\frac{\frac{81}{289}}{\frac{81}{160}}\right)^{-1}$$

Jagage \frac{81}{289} väärtusega \frac{81}{160}, korrutades \frac{81}{289} väärtuse \frac{81}{160} pöördväärtusega.

$$\left(\frac{81}{289}\times \frac{160}{81}\right)^{-1}$$

Korrutage \frac{81}{289} ja \frac{160}{81}, et leida \frac{160}{289}.

$$\left(\frac{160}{289}\right)^{-1}$$

Arvutage -1 aste \frac{160}{289} ja leidke \frac{289}{160}.

$$\frac{289}{160}$$

Lahuta teguriteks

$$\frac{17 ^ {2}}{2 ^ {5} \cdot 5} = 1\frac{129}{160} = 1,80625$$