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

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

I-evaluate

$$\frac{289}{160}=1.80625$$

Mga Hakbang ng Solution

Ipakita ang \frac{\frac{3}{9}}{3} bilang isang single fraction.

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

I-multiply ang 9 at 3 para makuha ang 27.

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

Bawasan ang fraction \frac{3}{27} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 3.

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

I-subtract ang \frac{1}{9} mula sa 2 para makuha ang \frac{17}{9}.

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

Kalkulahin ang \frac{17}{9} sa power ng -2 at kunin ang \frac{81}{289}.

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

Kalkulahin ang \frac{9}{4} sa power ng 2 at kunin ang \frac{81}{16}.

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

Kalkulahin ang 2 sa power ng -1 at kunin ang \frac{1}{2}.

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

Ipakita ang \frac{\frac{1}{2}}{5} bilang isang single fraction.

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

I-multiply ang 2 at 5 para makuha ang 10.

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

I-multiply ang \frac{81}{16} at \frac{1}{10} para makuha ang \frac{81}{160}.

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

I-divide ang \frac{81}{289} gamit ang \frac{81}{160} sa pamamagitan ng pagmu-multiply sa \frac{81}{289} gamit ang reciprocal ng \frac{81}{160}.

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

I-multiply ang \frac{81}{289} at \frac{160}{81} para makuha ang \frac{160}{289}.

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

Kalkulahin ang \frac{160}{289} sa power ng 1 at kunin ang \frac{160}{289}.

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

Kalkulahin ang \frac{160}{289} sa power ng -1 at kunin ang \frac{289}{160}.

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

I-factor

$$\frac{17 ^ {2}}{2 ^ {5} \cdot 5} = 1\frac{129}{160} = 1.80625$$