簡約 ((2^4)^2)^{-3}*(2^2)^{(2^2)^2}

解

簡約

((2^{4})^{2})^{- 3} \cdot (2^{2})^{(2^{2})^{2}}

256

解答ステップ

((2^{4})^{2})^{- 3} (2^{2})^{(2^{2})^{2}}

(2^{4})^{2} : 2^{8}

= (2^{8})^{- 3} (2^{2})^{(2^{2})^{2}}

(2^{2})^{(2^{2})^{2}} : 2^{32}

= (2^{8})^{- 3} \cdot 2^{32}

(2^{8})^{- 3} = \frac{1}{2 ^{24}}

= 2^{32} \cdot \frac{1}{2 ^{24}}

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2 ^{32}}{2 ^{24}}

乗算:

1 \cdot 2^{32} = 2^{32}

= \frac{2 ^{32}}{2 ^{24}}

指数の規則を適用する:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{2 ^{32}}{2 ^{24}} = 2^{32 - 24}

= 2^{32 - 24}

数を引く:

32 - 24 = 8

= 2^{8}

2^{8} = 256

= 256