Solve (10^-2)^2^2^2

$$( 10 ^ { - 2 } ) ^ { 2 ^ { 2 ^ { 2 } } }$$

Evaluate

$$\frac{1}{100000000000000000000000000000000}= 10^{-32}$$

Solution Steps

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

$$\left(\frac{1}{100}\right)^{2^{2^{2}}}$$

Calculate 2 to the power of 2 and get 4.

$$\left(\frac{1}{100}\right)^{2^{4}}$$

Calculate 2 to the power of 4 and get 16.

$$\left(\frac{1}{100}\right)^{16}$$

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

$$\frac{1}{100000000000000000000000000000000}$$

Factor

$$\frac{1}{2 ^ {32} \cdot 5 ^ {32}} = 0.9999999999999999 \times 10^{-32}$$