簡約 (8/5)^{-1/2}(2sqrt(5))^3(32^{4/5})^{-3/2}

解

簡約

(\frac{8}{5})^{- \frac{1}{2}} \cdot (25)^{3} \cdot (3 2^{\frac{4}{5}})^{- \frac{3}{2}}

5^{\frac{1}{2}} \cdot \frac{5 \cdot 5 ^{\frac{1}{2}}}{16 \cdot 2 ^{\frac{1}{2}}}

十進法表記

1.10485 \dots

解答ステップ

(\frac{8}{5})^{- \frac{1}{2}} (25)^{3} (3 2^{\frac{4}{5}})^{- \frac{3}{2}}

(\frac{8}{5})^{- \frac{1}{2}} = \frac{5 ^{\frac{1}{2}}}{2 \cdot 2 ^{\frac{1}{2}}}

= \frac{5 ^{\frac{1}{2}}}{2 \cdot 2 ^{\frac{1}{2}}} (25)^{3} (3 2^{\frac{4}{5}})^{- \frac{3}{2}}

(25)^{3} = 40 \cdot 5^{\frac{1}{2}}

= \frac{5 ^{\frac{1}{2}}}{2 \cdot 2 ^{\frac{1}{2}}} \cdot 40 \cdot 5^{\frac{1}{2}} (3 2^{\frac{4}{5}})^{- \frac{3}{2}}

(3 2^{\frac{4}{5}})^{- \frac{3}{2}} = \frac{1}{64}

= \frac{5 ^{\frac{1}{2}}}{2 \cdot 2 ^{\frac{1}{2}}} \cdot 40 \cdot 5^{\frac{1}{2}} \cdot \frac{1}{64}

\frac{5 ^{\frac{1}{2}}}{2 \cdot 2 ^{\frac{1}{2}}} \cdot 40 \cdot 5^{\frac{1}{2}} \cdot \frac{1}{64} = \frac{5 \cdot 5 ^{\frac{1}{2}}}{16 \cdot 2 ^{\frac{1}{2}}} \cdot 5^{\frac{1}{2}}

= \frac{5 \cdot 5 ^{\frac{1}{2}}}{16 \cdot 2 ^{\frac{1}{2}}} \cdot 5^{\frac{1}{2}}

= 5^{\frac{1}{2}} \cdot \frac{5 \cdot 5 ^{\frac{1}{2}}}{16 \cdot 2 ^{\frac{1}{2}}}