簡約 ((1-1/4)^2)^2

解

簡約

((1 - \frac{1}{4})^{2})^{2}

\frac{81}{256}

十進法表記

0.31640625

解答ステップ

((1 - \frac{1}{4})^{2})^{2}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}, a \geq 0

= (1 - \frac{1}{4})^{2 \cdot 2}

数を乗じる:

2 \cdot 2 = 4

= (1 - \frac{1}{4})^{4}

1 - \frac{1}{4} = \frac{3}{4}

= (\frac{3}{4})^{4}

指数の規則を適用する:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{3 ^{4}}{4 ^{4}}

3^{4} = 81

= \frac{81}{4 ^{4}}

4^{4} = 256

= \frac{81}{256}