簡約 sqrt(13.6)^{sqrt(13.6)}

解

簡約

13.6^{13.6}

\frac{2 ^{\frac{2 17}{5}} \cdot 1 7 ^{\frac{17}{5}}}{5 ^{\frac{17}{5}}}

十進法表記

123.06724 \dots

解答ステップ

(13.6)^{13.6}

13.6 = \frac{2 17}{5}

= (13.6)^{\frac{2 17}{5}}

13.6 = \frac{2 17}{5}

= (\frac{2 17}{5})^{\frac{2 17}{5}}

指数の規則を適用する:

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

= \frac{( 2 17 ) ^{\frac{2 17}{5}}}{( 5 ) ^{\frac{2 17}{5}}}

(217)^{\frac{2 17}{5}} = 2^{\frac{2 17}{5}} \cdot 1 7^{\frac{17}{5}}

= \frac{2 ^{\frac{2 17}{5}} \cdot 1 7 ^{\frac{17}{5}}}{( 5 ) ^{\frac{2 17}{5}}}

(5)^{\frac{2 17}{5}} = 5^{\frac{17}{5}}

= \frac{2 ^{\frac{2 17}{5}} \cdot 1 7 ^{\frac{17}{5}}}{5 ^{\frac{17}{5}}}