簡約 (\sqrt[4]{5x})^7

解

簡約

(4 5 x)^{7}

5 4 5^{3} 4 x^{7}

解答ステップ

(4 5 x)^{7}

指数の規則を適用する:

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

(4 5 x)^{4 + 3} = (4 5 x)^{4} (4 5 x)^{3}

= (4 5 x)^{4} (4 5 x)^{3}

指数の規則を適用する:

(n a)^{n} = a,

, 以下を想定

n i s o dd or a \geq 0

(4 5 x)^{4} = 5 x

= 5 x (4 5 x)^{3}

(4 5 x)^{3} = 5^{\frac{3}{4}} (4 x)^{3}

= 5 \cdot 5^{\frac{3}{4}} x (4 x)^{3}

指数の規則を適用する:

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

5 \cdot 5^{\frac{3}{4}} = 5^{1 + \frac{3}{4}}

= x \cdot 5^{1 + \frac{3}{4}} (4 x)^{3}

5^{1 + \frac{3}{4}} = 5 \cdot 5^{\frac{3}{4}}

= 5 \cdot 5^{\frac{3}{4}} x (4 x)^{3}

= 5^{\frac{3}{4}} \cdot 5 x (4 x)^{3}

簡素化

x (4 x)^{3} : x^{\frac{7}{4}}

= 5^{\frac{3}{4}} \cdot 5 x^{\frac{7}{4}}

5^{\frac{3}{4}} \cdot 5 = 5^{\frac{7}{4}}

= 5^{\frac{7}{4}} x^{\frac{7}{4}}

5^{\frac{7}{4}} = 5 \cdot 5^{\frac{3}{4}}

= 5 \cdot 5^{\frac{3}{4}} x^{\frac{7}{4}}

5^{\frac{3}{4}} = 4 5^{3}

= 5 4 5^{3} 4 x^{7}

x^{\frac{7}{4}} = 4 x^{7}

= 5 4 5^{3} 4 x^{7}