Solve (1-2*(2^4/5)^-1*2^3/5)^100

$$( 1 - 2 \cdot ( \frac { 2 ^ { 4 } } { 5 } ) ^ { - 1 } \cdot \frac { 2 ^ { 3 } } { 5 } ) ^ { 100 }$$

Evaluate

$$0$$

Solution Steps

Calculate 2 to the power of 4 and get 16.

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

Calculate \frac{16}{5} to the power of -1 and get \frac{5}{16}.

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

Multiply 2 and \frac{5}{16} to get \frac{5}{8}.

$$\left(1-\frac{5}{8}\times \frac{2^{3}}{5}\right)^{100}$$

Calculate 2 to the power of 3 and get 8.

$$\left(1-\frac{5}{8}\times \frac{8}{5}\right)^{100}$$

Multiply \frac{5}{8} and \frac{8}{5} to get 1.

$$\left(1-1\right)^{100}$$

Subtract 1 from 1 to get 0.

$$0^{100}$$

Calculate 0 to the power of 100 and get 0.

$$0$$

Factor

$$0$$