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

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

Evaluasi

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

Langkah Solusi

Hitung 10 sampai pangkat -5 dan dapatkan \frac{1}{100000}.

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

Tambahkan 3546 dan \frac{1}{100000} untuk mendapatkan \frac{354600001}{100000}.

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

Hitung \frac{354600001}{100000} sampai pangkat 9 dan dapatkan \frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}.

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

Hitung 10 sampai pangkat 2 dan dapatkan 100.

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

Kalikan 505 dan 100 untuk mendapatkan 50500.

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

Hitung 50500 sampai pangkat 12 dan dapatkan 275103767122062920083301025390625000000000000000000000000.

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

Nyatakan \frac{\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}}{275103767122062920083301025390625000000000000000000000000} sebagai pecahan tunggal.

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

Kalikan 1000000000000000000000000000000000000000000000 dan 275103767122062920083301025390625000000000000000000000000 untuk mendapatkan 275103767122062920083301025390625000000000000000000000000000000000000000000000000000000000000000000000.

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