Question

The digit in unit place of the product 2137⁷⁵⁴ is ??

please solve with process​

Answer 1

Answer:

The unit place of product of (2137) ⁷⁵⁴ is same as (7) ⁷⁵⁴

The unit digits of the powers of 7 are as follows:

7^1=7

7^2=9

7^3=3

7^4=1

7^5=7

7^6=9

so we can see that the cyclicity of the powers of 7 is 4

⇒ 7 ^ 188*4 + 2

Since 754 = 188*4 +2

⇒ 7^2 has unit place 9.

Therefore, the product of (7) ⁷⁵⁴ has unit place 9 and thus the product of (2137) ⁷⁵⁴ has unit place 9.

Answer 2

Answer:

9

Step-by-step explanation:

the unit place digits will be following

7¹=7

7²=9

7³=3

7⁴=1

these digits will repeat as the power increases

hence the power 754 is divide by 4 we will get the remainder 2

so the power should considered as 2

so the unit place digit will be 9