Lutasin ang 1600*(1/0.08-1/0.08*1.08^12)

$$1600 \times ( \frac{ 1 }{ 0.08 } - \frac{ 1 }{ 0.08 \times { 1.08 }^{ 12 } } )$$

I-evaluate

$$\frac{1809799810432169920000}{150094635296999121}\approx 12057.72482708$$

Mga Hakbang ng Solution

I-expand ang \frac{1}{0.08} sa pamamagitan ng pag-multiply sa parehong numerator at denominator ng 100.

$$1600\left(\frac{100}{8}-\frac{1}{0.08\times 1.08^{12}}\right)$$

Bawasan ang fraction \frac{100}{8} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 4.

$$1600\left(\frac{25}{2}-\frac{1}{0.08\times 1.08^{12}}\right)$$

Kalkulahin ang 1.08 sa power ng 12 at kunin ang 2.518170116818978404827136.

$$1600\left(\frac{25}{2}-\frac{1}{0.08\times 2.518170116818978404827136}\right)$$

I-multiply ang 0.08 at 2.518170116818978404827136 para makuha ang 0.20145360934551827238617088.

$$1600\left(\frac{25}{2}-\frac{1}{0.20145360934551827238617088}\right)$$

I-expand ang \frac{1}{0.20145360934551827238617088} sa pamamagitan ng pag-multiply sa parehong numerator at denominator ng 100000000000000000000000000.

$$1600\left(\frac{25}{2}-\frac{100000000000000000000000000}{20145360934551827238617088}\right)$$

Bawasan ang fraction \frac{100000000000000000000000000}{20145360934551827238617088} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 67108864.

$$1600\left(\frac{25}{2}-\frac{1490116119384765625}{300189270593998242}\right)$$

Ang least common multiple ng 2 at 300189270593998242 ay 300189270593998242. I-convert ang \frac{25}{2} at \frac{1490116119384765625}{300189270593998242} sa mga fraction na may denominator na 300189270593998242.

$$1600\left(\frac{3752365882424978025}{300189270593998242}-\frac{1490116119384765625}{300189270593998242}\right)$$

Dahil may parehong denominator ang \frac{3752365882424978025}{300189270593998242} at \frac{1490116119384765625}{300189270593998242}, ibawas ang mga ito sa pamamagitan ng pagbawas sa mga numerator ng mga ito.

$$1600\times \frac{3752365882424978025-1490116119384765625}{300189270593998242}$$

I-subtract ang 1490116119384765625 mula sa 3752365882424978025 para makuha ang 2262249763040212400.

$$1600\times \frac{2262249763040212400}{300189270593998242}$$

Bawasan ang fraction \frac{2262249763040212400}{300189270593998242} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 2.

$$1600\times \frac{1131124881520106200}{150094635296999121}$$

Ipakita ang 1600\times \frac{1131124881520106200}{150094635296999121} bilang isang single fraction.

$$\frac{1600\times 1131124881520106200}{150094635296999121}$$

I-multiply ang 1600 at 1131124881520106200 para makuha ang 1809799810432169920000.

$$\frac{1809799810432169920000}{150094635296999121}$$

I-factor

$$\frac{7 \cdot 13 \cdot 97 \cdot 677 \cdot 2029 \cdot 466441 \cdot 2 ^ {9} \cdot 5 ^ {4}}{3 ^ {36}} = 12057\frac{1.087926562513521 \times 10^{17}}{1.5009463529699913 \times 10^{17}} = 12057.724827080168$$