[A]ny matter relating to the business of the company may be exclusively decided by the manager or, if there is more than one manager, by a majority of the managers ... .See Section 404 of the Uniform Limited Liability Company Act. I can't think of a broader formulation of manager power.
However, certain matters are reserved by the default provision of the Uniform LLC Act for decision by the members such as the admission of a new member and the consent to dissolve the company. See Section 404(c). Remember that most of the LLC Act provisions can be altered by the operating agreement. A common feature of manager-managed LLC operating agreements is to reserve for member approval purchases or contract obligations (such as leases) above a certain dollar amount. I personally advocate putting such a check on the power of the managers. For a sample, see Section 4.3 of this manager-managed operating agreement.