[Vuejs]-Blank Page with Vuejs and Laravel

Based on the code you shared, you haven’t loaded any javascript files in your HTML. You should add the following line in either one of your blade files:
<script type="text/javascript" src="{{ asset('js/app.js') }}"></script>

I also don’t see you using your router.js-file anywhere, so you could import it in your app.js-file:
require('router.js');

If you don’t plan on using the existing app.js-file, you could just include router.js in your webpack.mix.js and load it in your HTML.