input: import re 
    
  def validate_numeric_string(string: str) -> bool:
      """ Check if the given string is a numeric string using a regular expression. 
      >>> validate_numeric_string('123456789')
      True
      >>> validate_numeric_string('abc123')
      False
      """
      pattern = '^[0-9]+$'
      result = re.match(pattern, string) 
      return bool(result)
output:     return bool(result)