Solve frac{(10^{-2})^{2^{2^{2}}}*[(10^{-2})^3^2^2]^-1}{5}

$$\frac { ( 10 ^ { - 2 } ) ^ { 2 ^ { 2 ^ { 2 } } } \cdot [ ( 10 ^ { - 2 } ) ^ { 3 ^ { 2 ^ { 2 } } } ] ^ { - 1 } } { 5 }$$

Evaluate

$$2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000$$

Solution Steps

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\frac{\left(\frac{1}{100}\right)^{2^{2^{2}}}\times \left(\left(10^{-2}\right)^{3^{2^{2}}}\right)^{-1}}{5}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\left(\frac{1}{100}\right)^{2^{4}}\times \left(\left(10^{-2}\right)^{3^{2^{2}}}\right)^{-1}}{5}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{\left(\frac{1}{100}\right)^{16}\times \left(\left(10^{-2}\right)^{3^{2^{2}}}\right)^{-1}}{5}$$

Calculate \frac{1}{100} to the power of 16 and get \frac{1}{100000000000000000000000000000000}.

$$\frac{\frac{1}{100000000000000000000000000000000}\times \left(\left(10^{-2}\right)^{3^{2^{2}}}\right)^{-1}}{5}$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\frac{\frac{1}{100000000000000000000000000000000}\times \left(\left(\frac{1}{100}\right)^{3^{2^{2}}}\right)^{-1}}{5}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\frac{1}{100000000000000000000000000000000}\times \left(\left(\frac{1}{100}\right)^{3^{4}}\right)^{-1}}{5}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{\frac{1}{100000000000000000000000000000000}\times \left(\left(\frac{1}{100}\right)^{81}\right)^{-1}}{5}$$

Calculate \frac{1}{100} to the power of 81 and get \frac{1}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{\frac{1}{100000000000000000000000000000000}\times \left(\frac{1}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\right)^{-1}}{5}$$

Calculate \frac{1}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} to the power of -1 and get 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{\frac{1}{100000000000000000000000000000000}\times 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{5}$$

Multiply \frac{1}{100000000000000000000000000000000} and 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 to get 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{5}$$

Divide 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 by 5 to get 2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000$$

Factor

$$2^{130}\times 5^{129}$$