public function update(Request $request, $id)
{
    $exploded = explode(',', request('image'));
    $decoded = base64_decode($exploded[1]);
    if(str_contains($exploded[0], 'jpeg'))
        $extension = 'jpg';
    else
        $extension = 'png';

    $fileName = str_random().'.'.$extension;
    $path = public_path().'/'.$fileName;
    file_put_contents($path, $decoded);

    $post = Post::findOrFail($id);
    $post->title = request('title');
    $post->description = request('description');
    $post->category_id = request('category_id');
    $post->user_id = Auth::id();
    $post->photo = $fileName;
    $post->save();

    return response()->json([
        'post' => $post,
    ], 200);
}

<div class="form-group">
  <label>Image</label>
  <input type="file" @change="imageChanged" class="form-control">
</div>

imageChanged(e){
   var fileReader = new FileReader()
   fileReader.readAsDataURL(e.target.files[0])
   fileReader.onload = (e) => {
      this.post.photo = e.target.result
   }
 },

editPost(){
  axios.patch('/api/posts/' + this.update_post.id, {
      title: this.update_post.title,
      description: this.update_post.description,
      category_id: this.update_post.category_id,
      photo: this.update_post.photo
  })
  .then(response => {
    this.showPosts();
  })
  .catch(function(error){
    console.log(error);
  });
}