簡約 (27a^{-3}b^6c^3)^{1/3}

解

簡約

(27 a^{- 3} b^{6} c^{3})^{\frac{1}{3}}

\frac{3 b ^{2} c}{a}

解答ステップ

(27 a^{- 3} b^{6} c^{3})^{\frac{1}{3}}

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

(27 a^{- 3} b^{6} c^{3})^{\frac{1}{3}} = 2 7^{\frac{1}{3}} (a^{- 3})^{\frac{1}{3}} (b^{6})^{\frac{1}{3}} (c^{3})^{\frac{1}{3}}

= 2 7^{\frac{1}{3}} (a^{- 3})^{\frac{1}{3}} (b^{6})^{\frac{1}{3}} (c^{3})^{\frac{1}{3}}

2 7^{\frac{1}{3}} = 3

= 3 (a^{- 3})^{\frac{1}{3}} (b^{6})^{\frac{1}{3}} (c^{3})^{\frac{1}{3}}

簡素化

(a^{- 3})^{\frac{1}{3}} : \frac{1}{a}

= 3 \cdot \frac{1}{a} (b^{6})^{\frac{1}{3}} (c^{3})^{\frac{1}{3}}

簡素化

(b^{6})^{\frac{1}{3}} : b^{2}

= 3 \cdot \frac{1}{a} b^{2} (c^{3})^{\frac{1}{3}}

簡素化

(c^{3})^{\frac{1}{3}} : c

= 3 \cdot \frac{1}{a} b^{2} c

簡素化

3 \cdot \frac{1}{a} b^{2} c : \frac{3 b ^{2} c}{a}

= \frac{3 b ^{2} c}{a}