Question

unit place of 4137^754​

Answer 1

Answer:

Step-by-step explanation:

By cyclicity after every 4 powers of a no. ending with 7, unit digit =1.

Hence unit digit of 4137^752=1

unit digit of 4137^753=1×7=7

unit digit of 4137^754=unit digit of 7×7= 9

Answer 2

Given:  

A number in exponential form 4137^754.  

To Find:  

The units digit of the above number.

Solution:  

1. The given number is$4137^{754}$  

2. The number can be also written as,  

=>$(4130+7)^{754}$,  

3. The units digit of the number$4130^{754}$ is 0. ( All the powers of the numbers ending with 0, have 0 as their units digit, except for power 0 which ends with 1 ).  

4. The units digit value  of 7^n is,  

• 7 for 4n+1 type values, (n can vary from 0 to infinite)

• 9 for 4n+2 type values,

• 3 for 4n+3 type values,

• 1 for 4n type values.

For example, the units digit of 7^4 is 3 as 4 can be also written as 4(1).

5. Using the property mentioned above the units digit of the number can be found,  

=> 754 = 4(188) + 2, ( 4n + 2 type value)  

=> Therefore, the units digit is 9.

=> Hence the units digit of the number $(4130+7)^{754}$is 0 + 9 = 9.

Therefore, the units digit of the number 4137^754  is 9.