Foreign keys not saved when trying to store data Laravel 8

I am trying to store store an author and genre into a Book. The way I’m trying to achieve this is by having an Author table, Genre table and a Book table. I want to store the foreign key for the author and genre into the books table.

I have created a form to store the needed information for the book. Within the form, there are two select tags and within them I loop through the authors and genres array. I use a store function in my BookController to validate the data that is being sent. After the validation, I store a new Book.

However, the foreign keys are not being stored in the database except for the primary key, title, blurb and timestamps.

Book Model

class Book extends Model
{
    use HasFactory;

    protected $fillable = [
        'author_id',
        'genre_id',
        'title',
        'blurb',
    ];

    public function authors()
    {
        return $this->BelongsTo(Author::class);
    }

    public function genres()
    {
        return $this->BelongsTo(Genre::class);
    }
}

Author Model

class Author extends Model
{
    use HasFactory;

    protected $fillable = [
      'name',
    ];

    public function book()
    {
        return $this->hasMany(Book::class);
    }
}

Genre Model

class Genre extends Model
{
    use HasFactory;

    protected $fillable = [
        'title'
    ];

    public function book()
    {
        return $this->hasMany(Book::class);
    }
}

BookController create()

    public function create()
    {
        $authors = Author::all();
        $genres = Genre::all();

        return view('admin.book.create', ['authors' => $authors, 'genres' => $genres]);
    }

BookController store()

    public function store(Request $request)
    {
        $validatedData = $request->validate([
            'title' => 'required|max:255',
            'authors' => 'required|array',
            'genres' => 'required|array',
            'blurb' => 'required',
        ]);

        Book::create($validatedData);

        return redirect()->route('admin.book.create');
    }

Books table migration

    public function up()
    {
        Schema::create('books', function (Blueprint $table) {
            $table->id();
            $table->foreignId('author_id');
            $table->foreignId('genre_id');
            $table->string('title');
            $table->string('blurb');
            $table->timestamps();
        });
    }

create.blade.php (create Book page)

    <div class="flex justify-center">
        <div class="flex justify-center border lg:w-1/4">
            <div class="flex flex-col justify-center lg:w-2/4 gap-2">
                <form action="{{ route('admin.book.store') }}" method="post">
                    @csrf
                    <div class="mb-2">
                        <h1 class="text-xl">Add Book</h1>
                    </div>
                    <div>
                        <label class="" for="title">Title</label>
                        <input name="title" class="w-10 border border-gray-400 w-full py-1 px-2" type="text">
                    </div>
                    <div>
                        <label class="" for="author">Author</label>
                        <select name="authors[]">
                            @foreach($authors as $author)
                                <option value="{{ $author->id }}">{{ $author->name }}</option>
                            @endforeach
                        </select>
                    </div>
                    <div>
                        <label class="" for="genre">Genre</label>
                        <select name="genres[]">
                            @foreach($genres as $genre)
                                <option value="{{ $genre->id }}">{{ $genre->title }}</option>
                            @endforeach
                        </select>
                    </div>
                    <div>
                        <label class="" for="blurb">Blurb</label>
                        <textarea name="blurb" id="" cols="18" rows="10"></textarea>
                    </div>
                    <div>
                        <button class="py-2 px-4 border" type="submit">Save</button>
                    </div>
                </form>
            </div>

        </div>
    </div>