Grade 12th passAlgebra
What is the last digit of the expression4x9^2x4^3x9^4x4^5x9^6x...........x4^99x9^100 ?
What is the last digit of the expression
4x9^2x4^3x9^4x4^5x9^6x...........x4^99x9^100 ?
1 Answer
archi
given expression=
(4*4^3 *4^5 *4^7 * … *4^99)*(9^2 *9^4 *9^6* 9^8 *... *9^100)................(i)
the last digit of all odd powers of 4 is 4.
therefore, in the first part of (i) multiplying all the last digits we get, 4*4*4*...=4^50 (there are 50 terms in that part)
the last digit of all even powers of 4 is 6.
therefore last digit of 4^50 is 6.
the last digit of all even powers of 9 is 1.
therefore, in the second part of (i) multiplying all the last digits we get, 1*1*1*...=1 (last digit =1)
multiplying the last digits, we get 6*1=6(ans.)
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