@ Kajin and Dejan0707
You are forgetting five key advantages that the USS Iowa has. First, it has radar-assisted fire control technology, so they would be able to score accurate shots on the Yamato from the guns' maximum range of 24 miles. Second, the armor-piercing 16-inch shell could easily punch through Yamato and do serious damage. The 16-inch AP shell could punch through up to but not including 18 inches of armor. The Yamato had 16 inches of side armor, 26 inches of armor on the face of the turrets, and between 7 and 9 inches of deck armor. While the Yamato's turrets would have been impenetrable, the rest of the ship could be easily damaged by the Iowa's guns. Third, the USS Iowa is faster and more maneuverable than the Yamato. The Iowa could easily dodge the Yamato's gunfire and still fire accurately thanks to her radar, whereas the Yamato's crew would have to hit a fast-moving target from miles away with their relatively primitive optical aiming devices. Fourth, the USS Iowa had superb damage control technology and crews. While a single 18-inch shell would devastate an Iowa-class, it would take a direct hit to a powder magazine to actually sink the ship. Fifth, the Yamato, her armor, and her shells were made of lower quality shells because of Japanese supply problems. The 18-inch shells on the Yamato would have less armor penetration ability than the 16-inch shells on the Iowa. Also, the Iowa's armor would be of a much higher quality and therefore more resilient than the Yamato's armor.
On paper, the Yamato appears to be the clear winner. However, upon further analysis, the Yamato has several severe handicaps that would cause her to be sunk by an Iowa-class.