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If `a,b,c` are three positive numbers then the minimum value of `(a^(4)+b^(6)+c^(8))/((ab^(3)c^(2))2sqrt(2))` is equal to_____

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The correct Answer is:
1
`((a^(4))/2+(a^(4))/2+(b^(6))/4+(b^(6))/3+(b^(6))/4+(b^(6))/4+(c^(8))/2+(c^(8))/2)/8 ge ((a^(8)b^(24)c^(16))/(2^(12)))^(1/8)`
Equality hold for `a=1, b=2^(1//6), c=1`
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