（１）
３乗の因数分解の公式
\(a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})\)
NAMO_EQN__ 160 1 a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})
より、
\((a^{^{\frac{1}{2}}}+a^{^{\frac{1}{4}}}b^{^{\frac{1}{4}}}+b^{^{\frac{1}{2}}})(a^{^{\frac{1}{2}}}-a^{^{\frac{1}{4}}}b^{^{\frac{1}{4}}}+b^{^{\frac{1}{2}}})=\frac{(a^{^{\frac{3}{4}}}-b^{^{\frac{3}{4}}})}{(a^{^{\frac{1}{4}}}-b^{^{\frac{1}{4}}})}\cdot \frac{(a^{^{\frac{3}{4}}}+b^{^{\frac{3}{4}}})}{(a^{^{\frac{1}{4}}}+b^{^{\frac{1}{4}}})}\)
NAMO_EQN__ 160 1 (a^{^{\frac{1}{2}}}+a^{^{\frac{1}{4}}}b^{^{\frac{1}{4}}}+b^{^{\frac{1}{2}}})(a^{^{\frac{1}{2}}}-a^{^{\frac{1}{4}}}b^{^{\frac{1}{4}}}+b^{^{\frac{1}{2}}})=\frac{(a^{^{\frac{3}{4}}}-b^{^{\frac{3}{4}}})}{(a^{^{\frac{1}{4}}}-b^{^{\frac{1}{4}}})}\cdot \frac{(a^{^{\frac{3}{4}}}+b^{^{\frac{3}{4}}})}{(a^{^{\frac{1}{4}}}+b^{^{\frac{1}{4}}})}
\(=\frac{a^{^{\frac{3}{2}}}-b^{^{\frac{3}{2}}}}{a^{^{\frac{1}{2}}}-b^{^{\frac{1}{2}}}}=a+a^{^{\frac{1}{2}}}b^{^{\frac{1}{2}}}+b\)
NAMO_EQN__ 160 1 =\frac{a^{^{\frac{3}{2}}}-b^{^{\frac{3}{2}}}}{a^{^{\frac{1}{2}}}-b^{^{\frac{1}{2}}}}=a+a^{^{\frac{1}{2}}}b^{^{\frac{1}{2}}}+b
………（答）
（２）
\((a^{^{\frac{x}{3}}}-b^{^{-\frac{x}{3}}})(a^{^{\frac{2x}{3}}}+a^{^{\frac{x}{3}}}b^{^{-\frac{x}{3}}}+b^{^{-\frac{2x}{3}}})=a^{x}-b^{-x}\)
NAMO_EQN__ 160 1 (a^{^{\frac{x}{3}}}-b^{^{-\frac{x}{3}}})(a^{^{\frac{2x}{3}}}+a^{^{\frac{x}{3}}}b^{^{-\frac{x}{3}}}+b^{^{-\frac{2x}{3}}})=a^{x}-b^{-x}
………（答）