簡約 (1/2)^{5+log_{2}(5)}

解

簡約

(\frac{1}{2})^{5 + l o g_{2} (5)}

\frac{1}{160}

十進法表記

0.00625

解答ステップ

(\frac{1}{2})^{5 + l o g_{2} (5)}

指数の規則を適用する:

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

(\frac{1}{2})^{5 + l o g_{2} (5)} = (\frac{1}{2})^{5} (\frac{1}{2})^{l o g_{2} (5)}

= (\frac{1}{2})^{5} (\frac{1}{2})^{l o g_{2} (5)}

(\frac{1}{2})^{5} = \frac{1}{32}

(\frac{1}{2})^{l o g_{2} (5)} = \frac{1}{5}

= \frac{1}{32} \cdot \frac{1}{5}

\frac{1}{32} \cdot \frac{1}{5} = \frac{1}{160}

= \frac{1}{160}