簡約 ln(10)(x^{1/3}y^{1/3}z^{1/3}) 1/x

解

簡約

ln (10) (x^{\frac{1}{3}} y^{\frac{1}{3}} z^{\frac{1}{3}}) \frac{1}{x}

\frac{ln ( 10 ) y ^{\frac{1}{3}} z ^{\frac{1}{3}}}{x ^{\frac{2}{3}}}

解答ステップ

ln (10) (x^{\frac{1}{3}} y^{\frac{1}{3}} z^{\frac{1}{3}}) \frac{1}{x}

指数の規則を適用する:

a^{m} b^{m} = (ab)^{m},

, 以下を想定

a \geq 0, b \geq 0

x^{\frac{1}{3}} y^{\frac{1}{3}} z^{\frac{1}{3}} = (x yz)^{\frac{1}{3}}

= ln (10) \frac{1}{x} (x yz)^{\frac{1}{3}}

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot ln ( 10 ) ( x yz ) ^{\frac{1}{3}}}{x}

乗算:

1 \cdot ln (10) = ln (10)

= \frac{ln ( 10 ) ( x yz ) ^{\frac{1}{3}}}{x}

因数

(x yz)^{\frac{1}{3}} : x^{\frac{1}{3}} y^{\frac{1}{3}} z^{\frac{1}{3}}

= \frac{ln ( 10 ) x ^{\frac{1}{3}} y ^{\frac{1}{3}} z ^{\frac{1}{3}}}{x}

キャンセル

\frac{ln ( 10 ) x ^{\frac{1}{3}} y ^{\frac{1}{3}} z ^{\frac{1}{3}}}{x} : \frac{ln ( 10 ) y ^{\frac{1}{3}} z ^{\frac{1}{3}}}{x ^{\frac{2}{3}}}

= \frac{ln ( 10 ) y ^{\frac{1}{3}} z ^{\frac{1}{3}}}{x ^{\frac{2}{3}}}