I have two similar expressions. The first expression can be simplified

$ 3125\ 2^{\frac{1}{2} \left(\sqrt{29}+5\right)} \left(7-\sqrt{29}\right)^{\frac{1}{2} \left(\sqrt{29}-7\right)} \left(\sqrt{29}-5\right)^{\frac{5}{2}-\frac{\sqrt{29}}{2}} \left(\sqrt{29}+3\right)^{-\frac{\sqrt{29}}{2}-\frac{3}{2}}$

`FullSimplify[3125 * 2^((1/2) * (5 + Sqrt[29])) * (7 - Sqrt[29])^((1/2)*(-7 + Sqrt[29])) * (-5 + Sqrt[29])^(5/2 - Sqrt[29]/2) * (3 + Sqrt[29])^(-(3/2) - Sqrt[29]/2)] (* 131 - 22 Sqrt[29] *) `

but the second expression not

$ 27\ 2^{\frac{1}{2} \left(\sqrt{13}+3\right)} \left(5-\sqrt{13}\right)^{\frac{1}{2} \left(\sqrt{13}-5\right)} \left(\sqrt{13}+1\right)^{\frac{1}{2} \left(-\sqrt{13}-1\right)} \left(\sqrt{13}-3\right)^{\frac{3}{2}-\frac{\sqrt{13}}{2}}$

`FullSimplify[27 2^(1/2 (3 + Sqrt[13])) (5 - Sqrt[13])^(1/2 (-5 + Sqrt[13])) (1 + Sqrt[13])^(1/2 (-1 - Sqrt[13])) (-3 + Sqrt[13])^(3/2 - Sqrt[13]/2)] (* 27 2^(1/2 (3 + Sqrt[13])) (5 - Sqrt[13])^(1/2 (-5 + Sqrt[13])) (-3 + Sqrt[13])^(3/2 - Sqrt[13]/2) (1 + Sqrt[13])^(1/2 (-1 - Sqrt[13])) *) `

Why ?

The requested result is

`(* 1/2 (11 + Sqrt[13]) *) `

The numerical check is OK:

`N[ 27 2^(1/2 (3 + Sqrt[13])) (5 - Sqrt[13])^(1/2 (-5 + Sqrt[13])) (1 + Sqrt[13])^(1/2 (-1 - Sqrt[13])) (-3 + Sqrt[13])^(3/2 - Sqrt[13]/2), 50] N[1/2 (11 + Sqrt[13]), 50] (* 7.3027756377319946465596106337352479731256482869226 *) (* 7.3027756377319946465596106337352479731256482869226 *) `