The notion of Single-valued neutrosophic sets (SVNSs) being a generalization of fuzzy sets, intuitionistic fuzzy sets and picture fuzzy sets  enhances implications of these methods in various interdisciplinary problems. Aggregation operator is a prevalent tool for unifying the data from various sources and applied to solve the problems of decision-making. In this article, the Yager's operations and power averaging operator are utilized to formulate and investigate some single-valued neutrosophic Yager power operators, i.e., single-valued neutrosophic Yager power weighted averaging (SVNYPWA) operators, single-valued neutrosophic Yager power order weighted averaging (SVNYPOWA) operator, single-valued neutrosophic Yager power weighted geometric averaging (SVNYPWGA) operator, and single-valued neutrosophic Yager power ordered weighted geometric averaging (SVNYPOWGA). Some important properties of the suggested operators are discussed. Furthermore, SVNYPWA and SVNYPWGA operators in the SVN environment are applied to solve the multi-criteria decision-making (MCDM) problem for selecting a suitable road construction company. Also, the proposed method has been verified using the multi-attributive border approximation area comparison (MABAC) method. Finally, a comparative analysis has been done, to establish the advantage of the proposed approach over the existing methods.