簡約 (343a^{12}b^{-3})^{2/3}

解

簡約

(343 a^{12} b^{- 3})^{\frac{2}{3}}

\frac{49 a ^{8}}{b ^{2}}

解答ステップ

(343 a^{12} b^{- 3})^{\frac{2}{3}}

指数の規則を適用する:

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

(343 a^{12} b^{- 3})^{\frac{2}{3}} = 34 3^{\frac{2}{3}} (a^{12})^{\frac{2}{3}} (b^{- 3})^{\frac{2}{3}}

= 34 3^{\frac{2}{3}} (a^{12})^{\frac{2}{3}} (b^{- 3})^{\frac{2}{3}}

34 3^{\frac{2}{3}} = 49

= 49 (a^{12})^{\frac{2}{3}} (b^{- 3})^{\frac{2}{3}}

簡素化

(a^{12})^{\frac{2}{3}} : a^{8}

= 49 a^{8} (b^{- 3})^{\frac{2}{3}}

簡素化

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

= 49 a^{8} \frac{1}{b ^{2}}

簡素化

49 a^{8} \frac{1}{b ^{2}} : \frac{49 a ^{8}}{b ^{2}}

= \frac{49 a ^{8}}{b ^{2}}