Ironic Isn't It?

\[ \large a^b = c^d = e^f = g^h = i^j = k^l \]

For distinct positive integers, \(a,b,c,d,e,f,g,h,i,j,k,l\) with \(a\) being the largest, the above equation is satisfied. What is the smallest possible value of \(a\)?

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