簡約 ((-54x^9)/(y^4))^{2/3}

解

簡約

(\frac{- 54 x ^{9}}{y ^{4}})^{\frac{2}{3}}

\frac{9 \cdot 2 ^{\frac{2}{3}} x ^{6}}{y ^{\frac{8}{3}}}

解答ステップ

(\frac{- 54 x ^{9}}{y ^{4}})^{\frac{2}{3}}

指数の規則を適用する:

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

= \frac{( - 54 x ^{9} ) ^{\frac{2}{3}}}{( y ^{4} ) ^{\frac{2}{3}}}

簡素化

(y^{4})^{\frac{2}{3}} : y^{\frac{8}{3}}

= \frac{( - 54 x ^{9} ) ^{\frac{2}{3}}}{y ^{\frac{8}{3}}}

(- 54 x^{9})^{\frac{2}{3}} = (54 x^{9})^{\frac{2}{3}}

= \frac{( 54 x ^{9} ) ^{\frac{2}{3}}}{y ^{\frac{8}{3}}}

(54 x^{9})^{\frac{2}{3}} = 3^{2} \cdot 2^{\frac{2}{3}} x^{6}

= \frac{3 ^{2} \cdot 2 ^{\frac{2}{3}} x ^{6}}{y ^{\frac{8}{3}}}

3^{2} = 9

= \frac{9 \cdot 2 ^{\frac{2}{3}} x ^{6}}{y ^{\frac{8}{3}}}