(25^{-1})/(5^{-2)}\div (0.5^{-2})/(0.1^{-3)}

解

\frac{2 5 ^{- 1}}{5 ^{- 2}} \div \frac{0. 5 ^{- 2}}{0. 1 ^{- 3}}

250

解答ステップ

\frac{2 5 ^{- 1}}{5 ^{- 2}} \div \frac{0. 5 ^{- 2}}{0. 1 ^{- 3}}

分数の規則を適用する:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

= \frac{2 5 ^{- 1}}{5 ^{- 2}} \times \frac{0. 1 ^{- 3}}{0. 5 ^{- 2}}

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

= 1 \times \frac{0. 1 ^{- 3}}{0. 5 ^{- 2}}

\frac{0. 1 ^{- 3}}{0. 5 ^{- 2}} = \frac{0. 5 ^{2}}{0. 1 ^{3}}

= 1 \times \frac{0. 5 ^{2}}{0. 1 ^{3}}

乗算:

1 \times \frac{0. 5 ^{2}}{0. 1 ^{3}} = \frac{0. 5 ^{2}}{0. 1 ^{3}}

= \frac{0. 5 ^{2}}{0. 1 ^{3}}

0. 5^{2} = 0.25

= \frac{0.25}{0. 1 ^{3}}

0. 1^{3} = 0.001

= \frac{0.25}{0.001}

数を割る:

\frac{0.25}{0.001} = 250

= 250