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

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

Vyhodnotit

$$\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{275103767122062920083301025390625000000000000000000000000000000000000000000000000000000000000000000000}\approx 3,222196748 \cdot 10^{-25}$$

Postup řešení

Výpočtem 10 na -5 získáte \frac{1}{100000}.

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

Sečtením 3546 a \frac{1}{100000} získáte \frac{354600001}{100000}.

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

Výpočtem \frac{354600001}{100000} na 9 získáte \frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}.

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

Výpočtem 10 na 2 získáte 100.

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

Vynásobením 505 a 100 získáte 50500.

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

Výpočtem 50500 na 12 získáte 275103767122062920083301025390625000000000000000000000000.

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

Vyjádřete \frac{\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}}{275103767122062920083301025390625000000000000000000000000} jako jeden zlomek.

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

Vynásobením 1000000000000000000000000000000000000000000000 a 275103767122062920083301025390625000000000000000000000000 získáte 275103767122062920083301025390625000000000000000000000000000000000000000000000000000000000000000000000.

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