簡約 (\sqrt[5]{x^2})/(\sqrt[6]{x^2)}

解

簡約

\frac{5 x ^{2}}{6 x ^{2}}

30 x^{2}

解答ステップ

\frac{5 x ^{2}}{6 x ^{2}}

累乗根の規則を適用する:

n a = a^{\frac{1}{n}}

5 x^{2} = (x^{2})^{\frac{1}{5}}

= \frac{( x ^{2} ) ^{\frac{1}{5}}}{6 x ^{2}}

累乗根の規則を適用する:

n a = a^{\frac{1}{n}}

6 x^{2} = (x^{2})^{\frac{1}{6}}

= \frac{( x ^{2} ) ^{\frac{1}{5}}}{( x ^{2} ) ^{\frac{1}{6}}}

指数の規則を適用する:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

= (x^{2})^{\frac{1}{5} - \frac{1}{6}}

結合

\frac{1}{5} - \frac{1}{6} : \frac{1}{30}

= 30 x^{2}