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Ketaksamaan pangkat-pangkatan

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Untuk semua $a,b,c$ riil positif, buktikan $a^ab^bc^c\geq\frac{2a+3b+3c}{8}^{\frac{3a+2b+3c}{8}}\frac{3a+2b+3c}{8}^{\frac{3a+3b+2c}{8}}\frac{3a+3b+2c}{8}^{\frac{2a+3b+3c}{8}}$


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