Many To Many Retreiving Book & Author Name Error Laravel

Unable to display all books name and author name as list. Getting error. If I return the books and authors variables in controller (index method) I get the data as array. But unable to access them in view. Also as mentioned in commented code (in Book Controller) below, code from laravel documentation shows error.

Book Model

class Book extends Model
{
 protected $guarded = [];

 public function authors(){
    return $this->belongsToMany('App\Models\Author')->withTimestamps();
 }
}

Author Model

class Author extends Model
{
 public $guarded = [];

 public function books(){
    return $this->belongsToMany('App\Models\Book')->withTimestamps();
 }
}

Book Controller

 public function index()
{
    $query = Book::with('authors')->get();
    Pls Read the commented lines below -
    //foreach ($query as $book) {
    //return $book->authors->author_name;  //Error: Property [author_name] does not exist on this collection instance.
    //}
    // (above code is given in laravel documentation but shows error : why?) 
    foreach($query as $b){
     $books[] = $b->book_name; 
     $authors[] = $b->authors->first()->author_name; 
    }
    return view('books.index', compact('books','authors'));
}

public function create()
{
    return view('books.create');
}

public function store(validateAuthorBook $request)
{
    $validated = $request->validated();
    if($validated){
        $book = new Book();
        $book->book_name = $request->book_name;
        $book->save();

        $author = new Author();
        $author->author_name = $request->author_name;
        $author->save();

        $book->authors()->attach($author);
    }

    return back()->with('status', 'Insert Successful!');
}

View (index.blade.php)

  @foreach($books as $b)
    <tr>
        <th>{{$loop->iteration}}</th>
        <td>{{$b->book_name}}</td>
        //<td>how to get author name</td>
        @endforeach
    </tr>

error

Facade\Ignition\Exceptions\ViewException
Trying to get property 'book_name' of non-object (View: 
D:\ProgrammingSSD\laragon\www\ulclibrary\resources\views\books\index.blade.php)

You are getting error because you are making $book a string in array ($books[] = $b->book_name;). You shouldn't do anything with $books collection in controller, and could send it directly to view.

Controller:

public function index()
{
    $books = Book::with('authors')->get();
    return view('books.index', compact('books'));
}

View (one line, split authors with comma):

@foreach($books as $book)
    <tr>
        <td>{{ $loop->iteration }}</td>
        <td>{{ $book->book_name }}</td>
        <td>{{ $book->authors->pluck('author_name')->implode(', ') }}</td>
    </tr>
@endforeach

View (loop, split authors with new line):

@foreach($books as $book)
    <tr>
        <td>{{ $loop->iteration }}</td>
        <td>{{ $book->book_name }}</td>
        <td>
            @foreach($book->authors as $author)
                {{ $author->author_name }}<br/>
            @endforeach
        </td>
    </tr>
@endforeach