# The minimum value of sum of real no a-^5,a^-4,3a^-3, 1, a^8 and a^10,with a>0,is

Solution: The given numbers are

$a^-5,a^-4, a^-3, a^-3, a^-3, 1, a^8 ;and;a^10$

We know that

$AM\geq GM\\ \\\Rightarrow 1/8(a^-5+a^-4+a^-3+a^-3+a^-3+a^0+a^8+a^10)\geq [(a^-5\times a^-4\times a^-3\times a^-3\times a^-3\times a^0\times a^8\times a^10)]^1/8\geq 1$

The Minimum value is 8

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