簡約 \sqrt[5]{ab}*\sqrt[3]{a^2b^2}

解

簡約

5 ab \cdot 3 a^{2} b^{2}

a^{\frac{13}{15}} b^{\frac{13}{15}}

解答ステップ

5 ab 3 a^{2} b^{2}

累乗根の規則を適用する:

n ab = n a n b

5 ab = 5 a 5 b

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

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

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

指数の規則を適用する:

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

5 a a^{\frac{2}{3}} = a^{\frac{1}{5}} a^{\frac{2}{3}} = a^{\frac{1}{5} + \frac{2}{3}}

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

指数の規則を適用する:

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

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

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

a^{\frac{1}{5} + \frac{2}{3}} = a^{\frac{13}{15}}

= a^{\frac{13}{15}} b^{\frac{1}{5} + \frac{2}{3}}

b^{\frac{1}{5} + \frac{2}{3}} = b^{\frac{13}{15}}

= a^{\frac{13}{15}} b^{\frac{13}{15}}