簡約 \sqrt[6]{3^5}*\sqrt[6]{3^5}

解

簡約

6 3^{5} \cdot 6 3^{5}

3 3 3^{2}

十進法表記

6.24025 \dots

解答ステップ

6 3^{5} 6 3^{5}

累乗根の規則を適用する:

n a = a^{\frac{1}{n}}

6 3^{5} = (3^{5})^{\frac{1}{6}}

= (3^{5})^{\frac{1}{6}} (3^{5})^{\frac{1}{6}}

指数の規則を適用する:

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

(3^{5})^{\frac{1}{6}} (3^{5})^{\frac{1}{6}} = (3^{5})^{\frac{1}{6} + \frac{1}{6}}

= (3^{5})^{\frac{1}{6} + \frac{1}{6}}

\frac{1}{6} + \frac{1}{6} = \frac{1}{3}

= (3^{5})^{\frac{1}{3}}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}, a \geq 0

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

5 \cdot \frac{1}{3} = \frac{5}{3}

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

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

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

指数の規則を適用する:

x^{a + b} = x^{a} x^{b}

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

改良

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

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

= 3 3 3^{2}