簡約 45^{3/2}*45^2

解

簡約

4 5^{\frac{3}{2}} \cdot 4 5^{2}

273375 \cdot 5^{\frac{1}{2}}

十進法表記

611285.08334 \dots

解答ステップ

4 5^{\frac{3}{2}} \cdot 4 5^{2}

指数の規則を適用する:

a^{b} \cdot a^{c} = a^{b + c}

4 5^{\frac{3}{2}} \cdot 4 5^{2} = 4 5^{\frac{3}{2} + 2}

= 4 5^{\frac{3}{2} + 2}

\frac{3}{2} + 2 = \frac{7}{2}

= 4 5^{\frac{7}{2}}

以下の素因数分解:

45 : 3^{2} \cdot 5

= (3^{2} \cdot 5)^{\frac{7}{2}}

指数の規則を適用する:

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

(3^{2} \cdot 5)^{\frac{7}{2}} = (3^{2})^{\frac{7}{2}} \cdot 5^{\frac{7}{2}}

= (3^{2})^{\frac{7}{2}} \cdot 5^{\frac{7}{2}}

(3^{2})^{\frac{7}{2}} = 2187

= 2187 \cdot 5^{\frac{7}{2}}

5^{\frac{7}{2}} = 5^{3} \cdot 5^{\frac{1}{2}}

= 5^{3} \cdot 2187 \cdot 5^{\frac{1}{2}}

5^{3} = 125

= 2187 \cdot 125 \cdot 5^{\frac{1}{2}}

数を乗じる:

2187 \cdot 125 = 273375

= 273375 \cdot 5^{\frac{1}{2}}