簡約 (81)^{-3/4}*(216)^{2/3}

解

簡約

(81)^{- \frac{3}{4}} \cdot (216)^{\frac{2}{3}}

\frac{4}{3}

十進法表記

1.33333 \dots

解答ステップ

8 1^{- \frac{3}{4}} \cdot 21 6^{\frac{2}{3}}

8 1^{- \frac{3}{4}} = \frac{1}{27}

= \frac{1}{27} \cdot 21 6^{\frac{2}{3}}

数を因数に分解する:

216 = 6^{3}

= \frac{1}{27} (6^{3})^{\frac{2}{3}}

指数の規則を適用する:

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

(6^{3})^{\frac{2}{3}} = 6^{3 \cdot \frac{2}{3}}

= \frac{1}{27} \cdot 6^{3 \cdot \frac{2}{3}}

3 \cdot \frac{2}{3} = 2

= \frac{1}{27} \cdot 6^{2}

6^{2} = 36

= \frac{1}{27} \cdot 36

\frac{1}{27} \cdot 36 = \frac{4}{3}

= \frac{4}{3}