The product-connectivity (also called Randić connectivity) index, sum-connectivity index and harmonic index are among the best-known and most successful vertex-degree-based topological indices in mathematical chemistry. The multiplicative versions of these graph invariants were proposed by Kulli in 2016. In this paper, we give the maximum values of the multiplicative product-connectivity, multiplicative sum-connectivity and multiplicative harmonic indices within the set of trees with a given order and maximum vertex degree and specify the maximal trees.