簡約 ((-2/6)^{-4})^2

解

簡約

((- \frac{2}{6})^{- 4})^{2}

6561

解答ステップ

((- \frac{2}{6})^{- 4})^{2}

指数の規則を適用する:

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

= (- \frac{2}{6})^{- 4 \cdot 2}

数を乗じる:

4 \cdot 2 = 8

= (- \frac{2}{6})^{- 8}

指数の規則を適用する:

a^{- b} = \frac{1}{a ^{b}}

(- \frac{2}{6})^{- 8} = \frac{1}{( - \frac{2}{6} ) ^{8}}

= \frac{1}{( - \frac{2}{6} ) ^{8}}

(- \frac{2}{6})^{8} = \frac{1}{6561}

= \frac{1}{\frac{1}{6561}}

\frac{1}{\frac{1}{6561}} = 6561

= 6561