Maths shortcut for finding units digit with exponent of base 3 and 7 are given in this post .Now u can solve a problem that is asked to find the units digits of given number with its units digit either 3 or 7.This amazing shortcut will cut your time in calculating the answer.If you are preparing for any competitive exam then this trick will help you most.Lets go straightly into knowing the trick with out wasting any time.Here i am going to assume a number with its units digit 3 as follows.
ASSUMED NUMBER IS (563)^155.Now you have to find the units digit for the number with exponent 155.It will be a tough ask when you don’t know this trick while calculating the answer.
Maths shortcut finding units digit of any exponent that ends with base 3 :
1.We have to find the units digit for the expression (563)^155 ?
- For finding the units digit of the above expression first of all we need to know the units digit for the power of 3 and they can be given as follows.
- (3^1=3) , (3^2=9) , (3^3=27) , (3^4=81) , (3^5=243) , (3^6=729) , and so on ………
- In the above step if you check the units digit they will be getting repeated after every four successful calculations.There will be a cyclicity of 4 for every unit digit to get repeated again.We need to remember the units digit 3,9,7,1.
- From the above given expression,155 is the exponent of base 3.Now we need to divide it by 4 ( as the cyclicity from the above step).The remainder will be 3.From the above step,we get 7 as the units digit.
- If the remainder is 1 then we need to take units digit as 3,if 2 then 9,if three then 7 and if the remainder is 0 then the units digit will be 1.Remember this point.Its important.
- Thus we calculate the units digit even if there is a large number present in the form of an exponent to a number with its unit digit as 3.
For more details regarding this math shortcut u can watch the video
In the same way you can calculate the unit digit of an exponent with its base as 7 the video of the same can be given as follows.
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