簡約 100(0.5^{1/32})^{39}

解

簡約

100 (0. 5^{\frac{1}{32}})^{39}

2^{\frac{25}{32}} \cdot 25

十進法表記

42.96548 \dots

解答ステップ

100 (0. 5^{\frac{1}{32}})^{39}

指数の規則を適用する:

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

(0. 5^{\frac{1}{32}})^{39} = 0. 5^{\frac{1}{32} \cdot 39}

= 100 \cdot 0. 5^{\frac{1}{32} \cdot 39}

\frac{1}{32} \cdot 39 = \frac{39}{32}

= 100 \cdot 0. 5^{\frac{39}{32}}

0.5 = \frac{1}{2}

= 100 (\frac{1}{2})^{\frac{39}{32}}

指数の規則を適用する:

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

(\frac{1}{2})^{\frac{39}{32}} = \frac{1 ^{\frac{39}{32}}}{2 ^{\frac{39}{32}}}

= 100 \cdot \frac{1 ^{\frac{39}{32}}}{2 ^{\frac{39}{32}}}

\frac{1 ^{\frac{39}{32}}}{2 ^{\frac{39}{32}}} = \frac{1}{2 \cdot 2 ^{\frac{7}{32}}}

= 100 \cdot \frac{1}{2 \cdot 2 ^{\frac{7}{32}}}

100 \cdot \frac{1}{2 \cdot 2 ^{\frac{7}{32}}} = 2^{\frac{25}{32}} \cdot 25

= 2^{\frac{25}{32}} \cdot 25