簡約 sqrt(\sqrt{\sqrt[7]{\sqrt[10]{16)}}}

解

簡約

71016

702

十進法表記

1.00995 \dots

解答ステップ

71016

71016 : 7016

= 7016

累乗根の規則を適用する:

a = a^{\frac{1}{2}}

= ((7016)^{\frac{1}{2}})^{\frac{1}{2}}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}

= (7016)^{\frac{1}{2} \cdot \frac{1}{2}}

\frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}

= (7016)^{\frac{1}{4}}

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

= 47016

累乗根の規則を適用する:

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

= (1 6^{\frac{1}{70}})^{\frac{1}{4}}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}

= 1 6^{\frac{1}{70} \cdot \frac{1}{4}}

\frac{1}{70} \cdot \frac{1}{4} = \frac{1}{280}

= 1 6^{\frac{1}{280}}

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

= 28016

28016 = 702

= 702