簡約 50^{3/2}

解

簡約

5 0^{\frac{3}{2}}

250 \cdot 2^{\frac{1}{2}}

十進法表記

353.55339 \dots

解答ステップ

5 0^{\frac{3}{2}}

以下の素因数分解:

50 : 2 \cdot 5^{2}

= (2 \cdot 5^{2})^{\frac{3}{2}}

指数の規則を適用する:

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

(2 \cdot 5^{2})^{\frac{3}{2}} = 2^{\frac{3}{2}} (5^{2})^{\frac{3}{2}}

= 2^{\frac{3}{2}} (5^{2})^{\frac{3}{2}}

(5^{2})^{\frac{3}{2}} = 125

= 2^{\frac{3}{2}} \cdot 125

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

= 2 \cdot 125 \cdot 2^{\frac{1}{2}}

数を乗じる:

2 \cdot 125 = 250

= 250 \cdot 2^{\frac{1}{2}}