Résoudre (3546+10^-5)^9/505*10^25^12

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

Évaluer

$$\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{12329101562500000000000000000000000000000000000000000000000}\approx 7,189805837 \cdot 10^{18}$$

Étapes de la solution

Calculer 10 à la puissance -5 et obtenir \frac{1}{100000}.

$$\frac{\left(3546+\frac{1}{100000}\right)^{9}}{505\times 10^{2}\times 5^{12}}$$

Additionner 3546 et \frac{1}{100000} pour obtenir \frac{354600001}{100000}.

$$\frac{\left(\frac{354600001}{100000}\right)^{9}}{505\times 10^{2}\times 5^{12}}$$

Calculer \frac{354600001}{100000} à la puissance 9 et obtenir \frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}.

$$\frac{\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}}{505\times 10^{2}\times 5^{12}}$$

Calculer 10 à la puissance 2 et obtenir 100.

$$\frac{\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}}{505\times 100\times 5^{12}}$$

Multiplier 505 et 100 pour obtenir 50500.

$$\frac{\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}}{50500\times 5^{12}}$$

Calculer 5 à la puissance 12 et obtenir 244140625.

$$\frac{\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}}{50500\times 244140625}$$

Multiplier 50500 et 244140625 pour obtenir 12329101562500.

$$\frac{\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}}{12329101562500}$$

Exprimer \frac{\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}}{12329101562500} sous la forme d’une fraction seule.

$$\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000\times 12329101562500}$$

Multiplier 1000000000000000000000000000000000000000000000 et 12329101562500 pour obtenir 12329101562500000000000000000000000000000000000000000000000.

$$\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{12329101562500000000000000000000000000000000000000000000000}$$