The Yak-9T did have very powerful cannon, however, read this paragraph from `Soviet Combat Aircraft of the Second World War: Volume 1: Single Engined Fighters' by Yefim Gordon and Dmitri Khazanov
ISBN 1 85780 083 4
`Pilot V. Khomyakov and armament engineer A. A. Aronov, who conducted flight tests of the Tak-9TK in October 1943, noted that the flying weight, centre of gravity position, handling qualites and performance varied in accordance with the gun installed (They were testing the 20mm ShVAK, the 23mm VYa, and the 37mm and the 45mm NS). When firing the ShVAK and VYa cannon the recoil was imperceptible even at minimum maneuvering speeds, whereas the recoil of the NS-37 greatly affected handling. At an indicated airspeed of 186 to 217 mph (300 to 350 km/h) the aircraft swung violently, and it was only possible to aim the first salvo. With the NS-45, only a single shot could be fired at near top speed.' pp-146
However, they began adding muzzle brakes to the cannons, and the Yak-9K was built with the 45mm NS. (29 shells). However, the plane wasn't very maneuverable in the vertical plane, and the book states that the great recoil caused many servicing problems, such as leaks etc. However, it could set a building, a ground vehicle, or locomotive on fire with a single shot! Ouch!
The Yak-9UT went into production with the 37mm cannon, but only saw action the last few days of the war over berlin according to the authors.