簡約 2.8944(0.9(0)+10)^{-0.7}

解

簡約

2.8944 (0.9 (0) + 10)^{- 0.7}

\frac{1809}{625 \cdot 1 0 ^{0.7}}

十進法表記

0.57750 \dots

解答ステップ

2.8944 (0.9 (0) + 10)^{- 0.7}

規則を適用する:

(a) = a

(0) = 0

= 2.8944 (0.9 \cdot 0 + 10)^{- 0.7}

指数の規則を適用する:

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

(0.9 \cdot 0 + 10)^{- 0.7} = \frac{1}{( 0.9 \cdot 0 + 10 ) ^{0.7}}

= 2.8944 \cdot \frac{1}{( 0.9 \cdot 0 + 10 ) ^{0.7}}

0.9 \cdot 0 + 10 = 10

= 2.8944 \cdot \frac{1}{1 0 ^{0.7}}

2.8944 \cdot \frac{1}{1 0 ^{0.7}} = \frac{2.8944}{1 0 ^{0.7}}

= \frac{2.8944}{1 0 ^{0.7}}

\frac{2.8944}{1 0 ^{0.7}} = \frac{28944}{10000 \cdot 1 0 ^{0.7}}

= \frac{28944}{10000 \cdot 1 0 ^{0.7}}

数を因数に分解する:

28944 = 16 \cdot 1809

= \frac{16 \cdot 1809}{10000 \cdot 1 0 ^{0.7}}

数を因数に分解する:

10000 = 16 \cdot 625

= \frac{16 \cdot 1809}{16 \cdot 625 \cdot 1 0 ^{0.7}}

共通因数を約分する:

16

= \frac{1809}{625 \cdot 1 0 ^{0.7}}