簡約 (3/5 a^6b^9)^2

解

簡約

(\frac{3}{5} a^{6} b^{9})^{2}

\frac{9 a ^{12} b ^{18}}{25}

解答ステップ

(\frac{3}{5} a^{6} b^{9})^{2}

指数の規則を適用する:

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

(\frac{3}{5} a^{6} b^{9})^{2} = (\frac{3}{5})^{2} (a^{6})^{2} (b^{9})^{2}

= (\frac{3}{5})^{2} (a^{6})^{2} (b^{9})^{2}

(\frac{3}{5})^{2} = \frac{9}{25}

= \frac{9}{25} (a^{6})^{2} (b^{9})^{2}

簡素化

(a^{6})^{2} : a^{12}

= \frac{9}{25} a^{12} (b^{9})^{2}

簡素化

(b^{9})^{2} : b^{18}

= \frac{9}{25} a^{12} b^{18}

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{9 a ^{12} b ^{18}}{25}