化简 sqrt(13.2)^{sqrt(13.2)}

解答

化简

13.2^{13.2}

10 \frac{6 6 ^{33}}{5 ^{33}}

十进制

108.54845 \dots

求解步骤

(13.2)^{13.2}

13.2 = \frac{66}{5}

= (13.2)^{\frac{66}{5}}

13.2 = \frac{66}{5}

= (\frac{66}{5})^{\frac{66}{5}}

使用根式运算法则:

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

= ((\frac{66}{5})^{\frac{1}{2}})^{\frac{66}{5}}

使用指数法则:

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

= (\frac{66}{5})^{\frac{1}{2} \frac{66}{5}}

\frac{1}{2} \frac{66}{5} = \frac{33}{10}

= (\frac{66}{5})^{\frac{33}{10}}

使用指数法则:

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

= \frac{6 6 ^{\frac{33}{10}}}{5 ^{\frac{33}{10}}}

5^{\frac{33}{10}} = 5^{\frac{33}{10}}

= \frac{6 6 ^{\frac{33}{10}}}{5 ^{\frac{33}{10}}}

6 6^{\frac{33}{10}} = 6 6^{\frac{33}{10}}

= \frac{6 6 ^{\frac{33}{10}}}{5 ^{\frac{33}{10}}}

合并相同指数项 :

\frac{x ^{\frac{a}{m}}}{y ^{\frac{b}{m}}} = m \frac{x ^{a}}{y ^{b}}

= (\frac{6 6 ^{33}}{5 ^{33}})^{\frac{1}{10}}

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