Решете (3546+10^-5)^9/505*10^25^12

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

Изчисляване

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

Стъпки на решението

Изчислявате -5 на степен 10 и получавате \frac{1}{100000}.

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

Съберете 3546 и \frac{1}{100000}, за да се получи \frac{354600001}{100000}.

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

Изчислявате 9 на степен \frac{354600001}{100000} и получавате \frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}.

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

Изчислявате 2 на степен 10 и получавате 100.

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

Умножете 505 по 100, за да получите 50500.

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

Изчислявате 12 на степен 5 и получавате 244140625.

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

Умножете 50500 по 244140625, за да получите 12329101562500.

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

Изразете \frac{\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}}{12329101562500} като една дроб.

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

Умножете 1000000000000000000000000000000000000000000000 по 12329101562500, за да получите 12329101562500000000000000000000000000000000000000000000000.

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