簡約 a{(24a^4b^3)/((sqrt(2a^2b)))}^{3/2}

解

簡約

a ⎩ ⎨ ⎧ \frac{24 a ^{4} \cdot b ^{3}}{( 2 a ^{2} \cdot b )} ⎭ ⎬ ⎫^{\frac{3}{2}}

2^{\frac{3}{4}} \cdot 3^{\frac{1}{2}} \cdot 24 a^{\frac{11}{2}} b^{\frac{15}{4}}

解答ステップ

a (\frac{24 a ^{4} b ^{3}}{2 a ^{2} b})^{\frac{3}{2}}

簡素化

(\frac{24 a ^{4} b ^{3}}{2 a ^{2} b})^{\frac{3}{2}} : 24 \cdot 2^{\frac{3}{4}} \cdot 3^{\frac{1}{2}} a^{\frac{9}{2}} b^{\frac{15}{4}}

= a \cdot 24 \cdot 2^{\frac{3}{4}} \cdot 3^{\frac{1}{2}} a^{\frac{9}{2}} b^{\frac{15}{4}}

簡素化

a a^{\frac{9}{2}} : a^{\frac{11}{2}}

= a^{\frac{11}{2}} \cdot 24 \cdot 2^{\frac{3}{4}} \cdot 3^{\frac{1}{2}} b^{\frac{15}{4}}

= 2^{\frac{3}{4}} \cdot 3^{\frac{1}{2}} \cdot 24 a^{\frac{11}{2}} b^{\frac{15}{4}}