There are version mismatch in your plunker which is causing that. Better to go for latest versions and their compatibility with each other.Check this plunkr
I added proper versioning
<script src="https://ajax.googleapis.com/ajax/libs/angularjs/1.6.1/angular.js"></script>
<script src="https://ajax.googleapis.com/ajax/libs/angularjs/1.6.1/angular-animate.js"></script>
<script src="https://ajax.googleapis.com/ajax/libs/angularjs/1.6.1/angular-sanitize.js"></script>
<script src="https://morgul.github.io/ui-bootstrap4/ui-bootstrap-tpls-3.0.3.min.js"></script>
<script src="example.js"></script>
<link href="https://netdna.bootstrapcdn.com/bootstrap/4.0.0/css/bootstrap.min.css" rel="stylesheet">
and accordingly modified html as per the directives of ui-bootstrap.
<div class="btn-group mb-2" uib-dropdown is-open="status.isopen">
<button id="single-button" type="button" class="btn btn-primary" uib-dropdown-toggle ng-disabled="disabled">
Button dropdown <span class="caret"></span>
</button>
<div class="dropdown-menu" uib-dropdown-menu role="menu" aria-labelledby="single-button">
<a href="#" class="dropdown-item">Action</a>
<a href="#" class="dropdown-item">Another action</a>
<a href="#" class="dropdown-item">Something else here</a>
<div class="dropdown-divider"></div>
<a href="#" class="dropdown-item">Separated link</a>
</div>
</div>
bootstrap.jsand jQuery. In general UI-Bootstrap fights jQuery and thebootstrap.js. Did you add them as a failed attempt to get UI-Bootstrap to work with Bootstrap 4 CSS?