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

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

Evaluasi

$$2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000$$

Langkah Solusi

Hitung 10 sampai pangkat -2 dan dapatkan \frac{1}{100}.

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

Hitung 2 sampai pangkat 2 dan dapatkan 4.

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

Hitung 2 sampai pangkat 4 dan dapatkan 16.

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

Hitung \frac{1}{100} sampai pangkat 16 dan dapatkan \frac{1}{100000000000000000000000000000000}.

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

Hitung 10 sampai pangkat -2 dan dapatkan \frac{1}{100}.

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

Hitung 2 sampai pangkat 2 dan dapatkan 4.

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

Hitung 3 sampai pangkat 4 dan dapatkan 81.

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

Hitung \frac{1}{100} sampai pangkat 81 dan dapatkan \frac{1}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

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

Hitung \frac{1}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} sampai pangkat -1 dan dapatkan 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

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

Kalikan \frac{1}{100000000000000000000000000000000} dan 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 untuk mendapatkan 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

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

Bagi 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 dengan 5 untuk mendapatkan 2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000$$

Faktor

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