簡約 (1/6 × 3/2)^5

解

簡約

(\frac{1}{6} \cdot \frac{3}{2})^{5}

\frac{1}{1024}

十進法表記

0.0009765625

解答ステップ

(\frac{1}{6} \cdot \frac{3}{2})^{5}

指数の規則を適用する:

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

(\frac{1}{6} \cdot \frac{3}{2})^{5} = (\frac{1}{6})^{5} (\frac{3}{2})^{5}

= (\frac{1}{6})^{5} (\frac{3}{2})^{5}

(\frac{1}{6})^{5} = \frac{1}{7776}

= \frac{1}{7776} (\frac{3}{2})^{5}

指数の規則を適用する:

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

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

= \frac{1}{7776} \cdot \frac{3 ^{5}}{2 ^{5}}

3^{5} = 243

= \frac{1}{7776} \cdot \frac{243}{2 ^{5}}

2^{5} = 32

= \frac{1}{7776} \cdot \frac{243}{32}

\frac{1}{7776} \cdot \frac{243}{32} = \frac{1}{1024}

= \frac{1}{1024}