簡約 (2310^{-2})^33010^{-3}9.8

解

簡約

(23 \cdot 1 0^{- 2})^{3} \cdot 30 \cdot 1 0^{- 3} \cdot 9.8

\frac{1788549}{500000000}

十進法表記

0.003577098

解答ステップ

(23 \cdot 1 0^{- 2})^{3} \cdot 30 \cdot 1 0^{- 3} \cdot 9.8

数を乗じる:

30 \cdot 9.8 = 294

= (23 \cdot 1 0^{- 2})^{3} \cdot 294 \cdot 1 0^{- 3}

= 1 0^{- 3} \cdot 294 (23 \cdot 1 0^{- 2})^{3}

1 0^{- 3} = \frac{1}{1000}

= \frac{1}{1000} \cdot 294 (23 \cdot 1 0^{- 2})^{3}

指数の規則を適用する:

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

(23 \cdot 1 0^{- 2})^{3} = 2 3^{3} (1 0^{- 2})^{3}

= \frac{1}{1000} \cdot 294 \cdot 2 3^{3} (1 0^{- 2})^{3}

2 3^{3} = 12167

= \frac{1}{1000} \cdot 294 \cdot 12167 (1 0^{- 2})^{3}

指数の規則を適用する:

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

(1 0^{- 2})^{3} = 1 0^{- 2 \cdot 3}

= \frac{1}{1000} \cdot 294 \cdot 12167 \cdot 1 0^{- 2 \cdot 3}

数を乗じる:

2 \cdot 3 = 6

= \frac{1}{1000} \cdot 294 \cdot 12167 \cdot 1 0^{- 6}

指数の規則を適用する:

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

1 0^{- 6} = \frac{1}{1 0 ^{6}}

= \frac{1}{1000} \cdot 294 \cdot 12167 \cdot \frac{1}{1 0 ^{6}}

1 0^{6} = 1000000

= \frac{1}{1000} \cdot 294 \cdot 12167 \cdot \frac{1}{1000000}

12167 \cdot \frac{1}{1000000} = \frac{12167}{1000000}

= \frac{1}{1000} \cdot 294 \cdot \frac{12167}{1000000}

\frac{1}{1000} \cdot 294 \cdot \frac{12167}{1000000} = \frac{1788549}{500000000}

= \frac{1788549}{500000000}