簡約 ((81^2)^{-8})^{1/3}

解

簡約

((8 1^{2})^{- 8})^{\frac{1}{3}}

\frac{1}{3 ^{21} \cdot 3 ^{\frac{1}{3}}}

十進法表記

6.62847 E - 11

解答ステップ

((8 1^{2})^{- 8})^{\frac{1}{3}}

(8 1^{2})^{- 8} : 8 1^{- 16}

= (8 1^{- 16})^{\frac{1}{3}}

指数の規則を適用する:

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

= 8 1^{(- 16) \frac{1}{3}}

(- 16) \frac{1}{3} = - \frac{16}{3}

= 8 1^{- \frac{16}{3}}

指数の規則を適用する:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{8 1 ^{\frac{16}{3}}}

8 1^{\frac{16}{3}} = (3 \cdot 3^{\frac{1}{3}})^{16}

= \frac{1}{( 3 \cdot 3 ^{\frac{1}{3}} ) ^{16}}

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

(3 \cdot 3^{\frac{1}{3}})^{16} = 3^{16} (3^{\frac{1}{3}})^{16}

= \frac{1}{3 ^{16} ( 3 ^{\frac{1}{3}} ) ^{16}}

(3^{\frac{1}{3}})^{16} : 3^{\frac{16}{3}}

= \frac{1}{3 ^{16} \cdot 3 ^{\frac{16}{3}}}

3^{\frac{16}{3}} = 3^{5} \cdot 3^{\frac{1}{3}}

= \frac{1}{3 ^{16} \cdot 3 ^{5} \cdot 3 ^{\frac{1}{3}}}

3^{16} \cdot 3^{5} \cdot 3^{\frac{1}{3}} = 3^{\frac{1}{3} + 21}

= \frac{1}{3 ^{\frac{1}{3} + 21}}

3^{\frac{1}{3} + 21} = 3^{21} \cdot 3^{\frac{1}{3}}

= \frac{1}{3 ^{21} \cdot 3 ^{\frac{1}{3}}}