簡約 12^{7/2}

解

簡約

1 2^{\frac{7}{2}}

3456 \cdot 3^{\frac{1}{2}}

十進法表記

5985.96759 \dots

解答ステップ

1 2^{\frac{7}{2}}

以下の素因数分解:

12 : 2^{2} \cdot 3

= (2^{2} \cdot 3)^{\frac{7}{2}}

指数の規則を適用する:

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

(2^{2} \cdot 3)^{\frac{7}{2}} = (2^{2})^{\frac{7}{2}} \cdot 3^{\frac{7}{2}}

= (2^{2})^{\frac{7}{2}} \cdot 3^{\frac{7}{2}}

(2^{2})^{\frac{7}{2}} = 128

= 128 \cdot 3^{\frac{7}{2}}

3^{\frac{7}{2}} = 3^{3} \cdot 3^{\frac{1}{2}}

= 3^{3} \cdot 128 \cdot 3^{\frac{1}{2}}

3^{3} = 27

= 128 \cdot 27 \cdot 3^{\frac{1}{2}}

数を乗じる:

128 \cdot 27 = 3456

= 3456 \cdot 3^{\frac{1}{2}}