簡約 0.074(21000000)^{-1/5}

解

簡約

0.074 (21000000)^{- \frac{1}{5}}

\frac{37}{5000 \cdot 21 0 ^{\frac{1}{5}}}

十進法表記

0.00253 \dots

解答ステップ

0.074 \cdot 2100000 0^{- \frac{1}{5}}

以下の素因数分解:

21000000 : 2^{6} \cdot 3 \cdot 5^{6} \cdot 7

= 0.074 (2^{6} \cdot 3 \cdot 5^{6} \cdot 7)^{- \frac{1}{5}}

指数の規則を適用する:

a^{b + c} = a^{b} \cdot a^{c}

2^{6} \cdot 3 \cdot 5^{6} \cdot 7 = 2^{5} \cdot 2 \cdot 3 \cdot 5^{5} \cdot 5 \cdot 7

= 0.074 (2^{5} \cdot 2 \cdot 3 \cdot 5^{5} \cdot 5 \cdot 7)^{- \frac{1}{5}}

= 0.074 (2^{5} \cdot 5^{5} \cdot 2 \cdot 3 \cdot 5 \cdot 7)^{- \frac{1}{5}}

指数の規則を適用する:

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

(2^{5} \cdot 5^{5} \cdot 2 \cdot 3 \cdot 5 \cdot 7)^{- \frac{1}{5}} = (2^{5})^{- \frac{1}{5}} (5^{5})^{- \frac{1}{5}} (2 \cdot 3 \cdot 5 \cdot 7)^{- \frac{1}{5}}

= 0.074 (2^{5})^{- \frac{1}{5}} (5^{5})^{- \frac{1}{5}} (2 \cdot 3 \cdot 5 \cdot 7)^{- \frac{1}{5}}

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

= 0.074 \cdot \frac{1}{2} (5^{5})^{- \frac{1}{5}} (2 \cdot 3 \cdot 5 \cdot 7)^{- \frac{1}{5}}

(5^{5})^{- \frac{1}{5}} = \frac{1}{5}

= 0.074 \cdot \frac{1}{2} \cdot \frac{1}{5} (2 \cdot 3 \cdot 5 \cdot 7)^{- \frac{1}{5}}

\frac{1}{2} \cdot \frac{1}{5} (2 \cdot 3 \cdot 5 \cdot 7)^{- \frac{1}{5}} = \frac{1}{10 \cdot 21 0 ^{\frac{1}{5}}}

= 0.074 \cdot \frac{1}{10 \cdot 21 0 ^{\frac{1}{5}}}

0.074 \cdot \frac{1}{10 \cdot 21 0 ^{\frac{1}{5}}} = \frac{0.074}{21 0 ^{\frac{1}{5}} \cdot 10}

= \frac{0.074}{21 0 ^{\frac{1}{5}} \cdot 10}

\frac{0.074}{21 0 ^{\frac{1}{5}} \cdot 10} = \frac{74}{10000 \cdot 21 0 ^{\frac{1}{5}}}

= \frac{74}{10000 \cdot 21 0 ^{\frac{1}{5}}}

数を因数に分解する:

74 = 2 \cdot 37

= \frac{2 \cdot 37}{10000 \cdot 21 0 ^{\frac{1}{5}}}

数を因数に分解する:

10000 = 2 \cdot 5000

= \frac{2 \cdot 37}{2 \cdot 5000 \cdot 21 0 ^{\frac{1}{5}}}

共通因数を約分する:

2

= \frac{37}{5000 \cdot 21 0 ^{\frac{1}{5}}}