Solve 2^100/2^10-1

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

Evaluate

$$\frac{1267650600228229401496703205376}{1023}\approx 1.239150147 \cdot 10^{27}$$

Solution Steps

Calculate 2 to the power of 100 and get 1267650600228229401496703205376.

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

Calculate 2 to the power of 10 and get 1024.

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

Subtract 1 from 1024 to get 1023.

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

Factor

$$\frac{2 ^ {100}}{3 \cdot 11 \cdot 31} = 1.239150146850664 \times 10^{27}\frac{1}{1023} = 1.239150146850664 \times 10^{27}$$