簡約-0.1sqrt(2^{-2)}(5\sqrt[3]{3^{-3}2})

解

簡約

- 0.1 2^{- 2} \cdot (5 3 3^{- 3} \cdot 2)

- \frac{1}{6 3 2 ^{2}}

十進法表記

- 0.10499 \dots

解答ステップ

- 0.1 2^{- 2} (5 3 3^{- 3} \cdot 2)

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

= - 0.1 \cdot \frac{1}{2} \cdot 5 3 3^{- 3} \cdot 2

累乗根の規則を適用する:

n ab = n a n b, a \geq 0, b \geq 0

3 3^{- 3} \cdot 2 = 3 3^{- 3} 32

= - 0.1 \cdot \frac{1}{2} \cdot 5 3 3^{- 3} 32

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

= - 0.1 \cdot \frac{1}{2} \cdot 5 \cdot \frac{1}{3} 32

\frac{1}{3} 32 = \frac{3 2}{3}

= - 0.1 \cdot \frac{1}{2} \cdot 5 \cdot \frac{3 2}{3}

数を乗じる:

- 0.1 \cdot 5 = - 0.5

= - 0.5 \cdot \frac{1}{2} \cdot \frac{3 2}{3}

= - \frac{1}{2} \cdot 0.5 \cdot \frac{3 2}{3}

0.5 = \frac{1}{2}

= - \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{3 2}{3}

- \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{3 2}{3} = - \frac{1}{6 \cdot 2 ^{\frac{2}{3}}}

= - \frac{1}{6 \cdot 2 ^{\frac{2}{3}}}

2^{\frac{2}{3}} = 3 2^{2}

= - \frac{1}{6 3 2 ^{2}}