MPK = 0.5 K^(-05) 16^0.5

MPK = 2 K^(-0.5)

Value of the marginal product = 8 K^(-0.5) (MPK multiplied with the price level)

Cost of capital = 1

so Value of MPK will equal Cost in optimum (first order condition of short term profit maximization)

K^0.5 = 8

K = 64

(hope I didn't make any miscalculations)