簡約 (2/3 x^5y^4)^3

解

簡約

(\frac{2}{3} x^{5} y^{4})^{3}

\frac{8 x ^{15} y ^{12}}{27}

解答ステップ

(\frac{2}{3} x^{5} y^{4})^{3}

指数の規則を適用する:

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

(\frac{2}{3} x^{5} y^{4})^{3} = (\frac{2}{3})^{3} (x^{5})^{3} (y^{4})^{3}

= (\frac{2}{3})^{3} (x^{5})^{3} (y^{4})^{3}

(\frac{2}{3})^{3} = \frac{8}{27}

= \frac{8}{27} (x^{5})^{3} (y^{4})^{3}

簡素化

(x^{5})^{3} : x^{15}

= \frac{8}{27} x^{15} (y^{4})^{3}

簡素化

(y^{4})^{3} : y^{12}

= \frac{8}{27} x^{15} y^{12}

分数を乗じる:

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

= \frac{8 x ^{15} y ^{12}}{27}