פתור את left(3546+10^-5right)^9/left(505*10^2right)^12

$$\frac{ { \left(3546+ { 10 }^{ -5 } \right) }^{ 9 } }{ { \left(505 \times { 10 }^{ 2 } \right) }^{ 12 } }$$

הערך

$$\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{275103767122062920083301025390625000000000000000000000000000000000000000000000000000000000000000000000}\approx 3.222196748 \cdot 10^{-25}$$

שלבי פתרון

חשב את 10 בחזקת -5 וקבל \frac{1}{100000}.

$$\frac{\left(3546+\frac{1}{100000}\right)^{9}}{\left(505\times 10^{2}\right)^{12}}$$

חבר את ‎3546 ו- ‎\frac{1}{100000} כדי לקבל ‎\frac{354600001}{100000}.

$$\frac{\left(\frac{354600001}{100000}\right)^{9}}{\left(505\times 10^{2}\right)^{12}}$$

חשב את \frac{354600001}{100000} בחזקת 9 וקבל \frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}.

$$\frac{\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}}{\left(505\times 10^{2}\right)^{12}}$$

חשב את 10 בחזקת 2 וקבל 100.

$$\frac{\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}}{\left(505\times 100\right)^{12}}$$

הכפל את ‎505 ו- ‎100 כדי לקבל ‎50500.

$$\frac{\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}}{50500^{12}}$$

חשב את 50500 בחזקת 12 וקבל 275103767122062920083301025390625000000000000000000000000.

$$\frac{\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}}{275103767122062920083301025390625000000000000000000000000}$$

בטא את ‎\frac{\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}}{275103767122062920083301025390625000000000000000000000000} כשבר אחד.

$$\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000\times 275103767122062920083301025390625000000000000000000000000}$$

הכפל את ‎1000000000000000000000000000000000000000000000 ו- ‎275103767122062920083301025390625000000000000000000000000 כדי לקבל ‎275103767122062920083301025390625000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{275103767122062920083301025390625000000000000000000000000000000000000000000000000000000000000000000000}$$