簡約 (7.8410^4)(1010^{-2}30*10^{-2})

解

簡約

(7.84 \cdot 1 0^{4}) \cdot (10 \cdot 1 0^{- 2} \cdot 30 \cdot 1 0^{- 2})

2352

解答ステップ

(7.84 \cdot 1 0^{4}) (10 \cdot 1 0^{- 2} \cdot 30 \cdot 1 0^{- 2})

7.84 \cdot 1 0^{4} = 78400

= 78400 \cdot 10 \cdot 1 0^{- 2} \cdot 30 \cdot 1 0^{- 2}

1 0^{- 2} = \frac{1}{100}

= 78400 \cdot 10 \cdot \frac{1}{100} \cdot 30 \cdot 1 0^{- 2}

指数の規則を適用する:

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

1 0^{- 2} = \frac{1}{1 0 ^{2}}

= 78400 \cdot 10 \cdot \frac{1}{100} \cdot 30 \cdot \frac{1}{1 0 ^{2}}

1 0^{2} = 100

= 78400 \cdot 10 \cdot \frac{1}{100} \cdot 30 \cdot \frac{1}{100}

数を乗じる:

78400 \cdot 10 \cdot 30 = 23520000

= 23520000 \cdot \frac{1}{100} \cdot \frac{1}{100}

指数の規則を適用する:

aa = a^{2}

\frac{1}{100} \cdot \frac{1}{100} = (\frac{1}{100})^{2}

= 23520000 (\frac{1}{100})^{2}

指数の規則を適用する:

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

(\frac{1}{100})^{2} = \frac{1 ^{2}}{10 0 ^{2}}

= 23520000 \cdot \frac{1 ^{2}}{10 0 ^{2}}

1^{2} = 1

= 23520000 \cdot \frac{1}{10 0 ^{2}}

10 0^{2} = 10000

= 23520000 \cdot \frac{1}{10000}

23520000 \cdot \frac{1}{10000} = 2352

= 2352