Question

find the rightmost non integer of the expression 1430^343+1470^367

Answer 1

Right most nonzero digit in
3^1 = 3
3^2 = 9
3^3= 7
3^4 = 1

30^5= 3
and the pattern (3,9,7,1) repeats
1430^343= 1430^4(85)+3
So it's rightmost nonzero digit= 7

Right most nonzero digit in
7^1 = 7
7^2 = 9
7^3= 3
7^4 = 1

30^5= 3
and the pattern (7,9,3,1) repeats
1470^367= 1430^4(91) + 3
So it's rightmost nonzero digit= 3

Adding both 7 + 3 = 10
so the right most nonzero digit is 1

Answer 2

Answer:

The right most non zero integer in given series is 7

Step-by-step explanation:

The correct question is "find the rightmost non zero integer of the expression 1430^343+1470^367

The given expression is

${1430}^{343} + {1470}^{367}$

The first term in the expression has 343 zeros and the second term has 367 zeros.Since,the 1st term is having less number of zeros compared to second term,to find the right most non zero integer,analysing 1st term is enough.The first term is

${1430}^{343}$

As ignore zero,our answer depends on 3 hence

${3}^{343}$

This can be written as

${3}^{4(85) + 3}$

Hence its of form

${3}^{4k + 3}$

Hence in the power series of 3,we get

$3 {}^{3} = 27 \\ last \: digit = 7$

Therefore,the right most non zero integer in given series is 7

#SPJ2