Resolver 2^100/2^10-1

$$\frac { 2 ^ { 100 } } { 2 ^ { 10 } - 1 }$$

Avaliar

$$\frac{1267650600228229401496703205376}{1023}\approx 1,239150147 \cdot 10^{27}$$

Passos Para a Resolução

Calcule 2 elevado a 100 e obtenha 1267650600228229401496703205376.

$$\frac{1267650600228229401496703205376}{2^{10}-1}$$

Calcule 2 elevado a 10 e obtenha 1024.

$$\frac{1267650600228229401496703205376}{1024-1}$$

Subtraia 1 de 1024 para obter 1023.

$$\frac{1267650600228229401496703205376}{1023}$$

Fatorizar

$$\frac{2 ^ {100}}{3 \cdot 11 \cdot 31} = 1,239150146850664 \times 10^{27}\frac{1}{1023} = 1,239150146850664 \times 10^{27}$$