簡約 (\sqrt[11]{x^9})/(\sqrt[4]{x^3)}

解

簡約

\frac{11 x ^{9}}{4 x ^{3}}

\frac{4 x 11 x ^{9}}{x}

解答ステップ

\frac{11 x ^{9}}{4 x ^{3}}

共役で乗じる

\frac{( x ^{3} ) ^{\frac{3}{4}}}{( x ^{3} ) ^{\frac{3}{4}}}

= \frac{11 x ^{9} ( x ^{3} ) ^{\frac{3}{4}}}{4 x ^{3} ( x ^{3} ) ^{\frac{3}{4}}}

簡素化

11 x^{9} (x^{3})^{\frac{3}{4}} : x^{\frac{9}{4}} 11 x^{9}

4 x^{3} (x^{3})^{\frac{3}{4}} = x^{3}

= \frac{x ^{\frac{9}{4}} 11 x ^{9}}{x ^{3}}

x^{\frac{9}{4}} = x^{2 + \frac{1}{4}}, x^{3} = x^{2 + 1}

= \frac{x ^{\frac{1}{4} + 2} 11 x ^{9}}{x ^{2 + 1}}

指数の規則を適用する:

a^{b + c} = a^{b} a^{c}

x^{2 + \frac{1}{4}} = x^{2} x^{\frac{1}{4}}, x^{2 + 1} = x^{2} x^{1}

= \frac{x ^{2} x ^{\frac{1}{4}} 11 x ^{9}}{x ^{2} x ^{1}}

共通因数を約分する:

x^{2}

= \frac{x ^{\frac{1}{4}} 11 x ^{9}}{x}

x^{\frac{1}{4}} = 4 x

= \frac{4 x 11 x ^{9}}{x}