簡約 (3x^{2/3})(3x^{1/3})

解

簡約

(3 x^{\frac{2}{3}}) (3 x^{\frac{1}{3}})

9 x

解答ステップ

(3 x^{\frac{2}{3}}) (3 x^{\frac{1}{3}})

指数の規則を適用する:

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

3 \cdot 3 = 3^{1 + 1}

= x^{\frac{2}{3}} \cdot 3^{1 + 1} x^{\frac{1}{3}}

数を足す:

1 + 1 = 2

= x^{\frac{2}{3}} \cdot 3^{2} x^{\frac{1}{3}}

指数の規則を適用する:

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

x^{\frac{2}{3}} x^{\frac{1}{3}} = x^{\frac{2}{3} + \frac{1}{3}}

= 3^{2} x^{\frac{2}{3} + \frac{1}{3}}

分数を組み合わせる

\frac{2}{3} + \frac{1}{3} : 1

= 3^{2} x^{1}

規則を適用

a^{1} = a

x^{1} = x

= 3^{2} x

3^{2} = 9

= 9 x