求解。高中数学分数指数幂
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原式={[a^(1/3)(a-8b)]/[4b^(2/3)+2(ab)^(1/3)+a^(2/3)]}×{[a^(1/3)]/[a^(1/3)-2b^(1/3)]}×[a^(1/3)]
=a(a-8b)/{[4b^(2/3)+2(ab)^(1/3)+a^(2/3)][a^(1/3)-2b^(1/3)]}=a(a-8b)/(a-8b)=a
其中分母=[4b^(2/3)+2(ab)^(1/3)+a^(2/3)][a^(1/3)-2b^(1/3)]
=4a^(1/3)b^(2/3)+2a^(2/3)b^(1/3)+a-8b-4a^(1/3)b^(2/3)-2a^(2/3)b^(1/3)=a-8b
=a(a-8b)/{[4b^(2/3)+2(ab)^(1/3)+a^(2/3)][a^(1/3)-2b^(1/3)]}=a(a-8b)/(a-8b)=a
其中分母=[4b^(2/3)+2(ab)^(1/3)+a^(2/3)][a^(1/3)-2b^(1/3)]
=4a^(1/3)b^(2/3)+2a^(2/3)b^(1/3)+a-8b-4a^(1/3)b^(2/3)-2a^(2/3)b^(1/3)=a-8b
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