Question

what is the unit digit of 37^33-33^37 ?​

Answer 1

Answer:

unit digit of 37³³ - 33³⁷ would be 4

Step-by-step explanation:

unit digit of 37^33-33^37

37³³

= ((37)³)¹¹

Here we will be only concentrating on unit digit

7³ end with 3

= (3)¹¹

= 3⁸ * 3³

= (3⁴)² * 3³

3⁴ end with 1

= 1² * 27

Hence unit  digit of 37³³ would be 7

33³⁷

= 33³⁶  * 3

= ((33)⁴)⁹ * 3

3⁴ ends with 1

= 1⁹ * 3

= 3

Hence unit  digit of 33³⁷ would be 3

37³³ - 33³⁷

= 7 - 3 = 4

unit digit of 37³³ - 33³⁷ would be 4