How to find Unit Place Digit Phase 2

We have already found the units place digit for some numbers like 0, 1, 5, 6 and 2. So far we have seen that there are some numbers for which we don’t need any explanation to find out their units place digit.

Here we come to find the units place digit of 3, 4, 8, and 7.

Let’s take a look:

If Units place digit is 4 or 8, then we should first divide the power by 4 and then represent in the form of 4⁴ or 8⁴. In that case the value of 4⁴ and 8⁴ will be 6. [Because 4*4*4*4 = 256 or 8*8*8*8 = 4096]

       (124)³⁷²    = (4) ^(372/4)  

                         = (4⁴)⁹³

                         = 4⁴ = 256                                   

       (128)³²⁵     = (8) ^(324/4)

                          = (8⁴)⁸¹

                          = 8⁴ = 4096

So the unit place digit is 6.

Again, if the unit place digit is 3 or 7, then we should first divide the power by 4 and then represent in the form of 3⁴ and 7⁴. In that case the value of 3⁴ and 7⁴ will be 1.                                                                  

        (2467)¹⁵³   = (7) ^(153/4)                    

                          = (7⁴)³⁸ * 7¹                                 

                           = 7⁴ * 7                                        

                          = 1 * 7 = 7                                  

                      [7⁴ = 7*7*7*7 = 2401]                               

       (293)¹⁴¹     = (3) ^(141/4)

                          = (3⁴)³⁵ * 3¹

                          = 3⁴ * 3

                          = 1 * 3 = 3

                      [3⁴ = 3*3*3*3 = 81]

 So the unit place digits are 7 and 3 respectively.