簡約 1.2558(3(10^9))^{-0.0178}

解

簡約

1.2558 (3 (1 0^{9}))^{- 0.0178}

\frac{6279}{5000 \cdot 3 ^{0.0178} \cdot 1 0 ^{0.1602}}

十進法表記

0.85158 \dots

解答ステップ

1.2558 (3 (1 0^{9}))^{- 0.0178}

規則を適用する:

(a) = a

(1 0^{9}) = 1 0^{9}

= 1.2558 (3 \cdot 1 0^{9})^{- 0.0178}

指数の規則を適用する:

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

(3 \cdot 1 0^{9})^{- 0.0178} = \frac{1}{( 3 \cdot 1 0 ^{9} ) ^{0.0178}}

= 1.2558 \cdot \frac{1}{( 3 \cdot 1 0 ^{9} ) ^{0.0178}}

(3 \cdot 1 0^{9})^{0.0178} = 3^{0.0178} \cdot 1 0^{0.1602}

= 1.2558 \cdot \frac{1}{3 ^{0.0178} \cdot 1 0 ^{0.1602}}

1.2558 \cdot \frac{1}{3 ^{0.0178} \cdot 1 0 ^{0.1602}} = \frac{1.2558}{3 ^{0.0178} \cdot 1 0 ^{0.1602}}

= \frac{1.2558}{3 ^{0.0178} \cdot 1 0 ^{0.1602}}

\frac{1.2558}{3 ^{0.0178} \cdot 1 0 ^{0.1602}} = \frac{12558}{10000 \cdot 3 ^{0.0178} \cdot 1 0 ^{0.1602}}

= \frac{12558}{10000 \cdot 3 ^{0.0178} \cdot 1 0 ^{0.1602}}

数を因数に分解する:

12558 = 2 \cdot 6279

= \frac{2 \cdot 6279}{10000 \cdot 3 ^{0.0178} \cdot 1 0 ^{0.1602}}

数を因数に分解する:

10000 = 2 \cdot 5000

= \frac{2 \cdot 6279}{2 \cdot 5000 \cdot 3 ^{0.0178} \cdot 1 0 ^{0.1602}}

共通因数を約分する:

2

= \frac{6279}{5000 \cdot 3 ^{0.0178} \cdot 1 0 ^{0.1602}}