簡約 (sqrt(36/49))^{3/2}

解

簡約

(\frac{36}{49})^{\frac{3}{2}}

\frac{6 \cdot 6 ^{\frac{1}{2}}}{7 \cdot 7 ^{\frac{1}{2}}}

十進法表記

0.79356 \dots

解答ステップ

(\frac{36}{49})^{\frac{3}{2}}

\frac{36}{49} = \frac{6}{7}

= (\frac{6}{7})^{\frac{3}{2}}

指数の規則を適用する:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{6 ^{\frac{3}{2}}}{7 ^{\frac{3}{2}}}

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

= \frac{6 ^{\frac{3}{2}}}{7 \cdot 7 ^{\frac{1}{2}}}

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

= \frac{6 \cdot 6 ^{\frac{1}{2}}}{7 \cdot 7 ^{\frac{1}{2}}}