the unit digit 17^2009+11^2009-7^2009is
Answers
Answer:
The answer of the above question is 1 .
Given:
A mathematical expression 17^2009+11^2009-7^2009.
To Find:
The units digit of the above expression.
Solution:
The given problem can be solved using the concepts of powers of units digit.
1. The given expression is 17^2009+11^2009-7^2009.
2. The units digit of 17^ 2009 is equal to the units of 7 ^ 2009. ( 17^ 2009 can be also written as (10 + 7 ) ^ 2009.
3. 10^ 2009 always end with 0 because powers of 10 always end with 0. The units digit of 7^2009 can be calculated as,
=> 7 ^ 1 ends with units digit 7,
=> 7 ^ 2 ends with units digit 9,
=> 7 ^ 3 ends with units digit 3,
=> For values 4n + 1, 7^n ends with 7,
=> For values 4n + 2, 7^n ends with 9,
=> For values 4n + 3, 7^n ends with 3,
=> For values 4n , 7^n ends with 1,
4. 2009 can be written as 4 x 502 + 1. Therefore, the units digit of 7^2009 is 7.
5. The units digit of 11^2009 is,
=> For any values of n the value of 11^n ends with 1 only.
=> The units digit is always 1 for any value of 1 including 0.
=> Therefore, the value of units digit of 11^2009 is 1.
6. 7^2009 ends with a units digit of 7 ( same as for 17^2009 ).
7. Therefore, the units digit of the expression 17^2009+11^2009-7^2009 is,
=> 7 + 1 - 7,
=> 1.
Therefore, the units digit of the expression 17^2009+11^2009-7^2009 is 1.