簡約 a/(\sqrt[6]{b^2)}

解

簡約

\frac{a}{6 b ^{2}}

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

解答ステップ

\frac{a}{6 b ^{2}}

共役で乗じる

\frac{( b ^{2} ) ^{\frac{5}{6}}}{( b ^{2} ) ^{\frac{5}{6}}}

= \frac{a ( b ^{2} ) ^{\frac{5}{6}}}{6 b ^{2} ( b ^{2} ) ^{\frac{5}{6}}}

簡素化

a (b^{2})^{\frac{5}{6}} : a b^{\frac{5}{3}}

6 b^{2} (b^{2})^{\frac{5}{6}} = b^{2}

= \frac{a b ^{\frac{5}{3}}}{b ^{2}}

b^{\frac{5}{3}} = b^{1 + \frac{2}{3}}, b^{2} = b^{1 + 1}

= \frac{a b ^{\frac{2}{3} + 1}}{b ^{1 + 1}}

指数の規則を適用する:

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

b^{1 + \frac{2}{3}} = b^{1} b^{\frac{2}{3}}, b^{1 + 1} = b^{1} b^{1}

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

共通因数を約分する:

b^{1}

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