Step-by-step explanation:
To find the unit digit of the expression
125
3
1469
−
8
1471
1253
−1258
, we can observe a pattern related to the unit digits of powers of 3 and 8.
For powers of 3, the unit digit follows the pattern: 3, 9, 7, 1, 3, 9, 7, 1, ...
For powers of 8, the unit digit follows the pattern: 8, 4, 2, 6, 8, 4, 2, 6, ...
Now, let's analyze the given expression:
The unit digit of
depends on the unit digit of 3 raised to the power of 1469, which is the 1469th term in the pattern of 3, 9, 7, 1, ... Since
m
o
d
4
=
1
1469mod4=1, the unit digit of
is 3.
1258
depends on the unit digit of 8 raised to the power of 1471, which is the 1471st term in the pattern of 8, 4, 2, 6, ... Since
1471mod4=3, the unit digit of
is 2.
Now, subtracting the unit digit of
from the unit digit of
:
2
3−2=1
So, the unit digit of the expression
is 1.
Therefore, the correct answer is option A. 1.
Answer- B. (9) Here's the answer of your question.
Copyright © 2024 EHUB.TIPS team's - All rights reserved.
Answers & Comments
Step-by-step explanation:
To find the unit digit of the expression
125
3
1469
−
125
8
1471
1253
1469
−1258
1471
, we can observe a pattern related to the unit digits of powers of 3 and 8.
For powers of 3, the unit digit follows the pattern: 3, 9, 7, 1, 3, 9, 7, 1, ...
For powers of 8, the unit digit follows the pattern: 8, 4, 2, 6, 8, 4, 2, 6, ...
Now, let's analyze the given expression:
The unit digit of
125
3
1469
1253
1469
depends on the unit digit of 3 raised to the power of 1469, which is the 1469th term in the pattern of 3, 9, 7, 1, ... Since
1469
m
o
d
4
=
1
1469mod4=1, the unit digit of
125
3
1469
1253
1469
is 3.
The unit digit of
125
8
1471
1258
1471
depends on the unit digit of 8 raised to the power of 1471, which is the 1471st term in the pattern of 8, 4, 2, 6, ... Since
1471
m
o
d
4
=
3
1471mod4=3, the unit digit of
125
8
1471
1258
1471
is 2.
Now, subtracting the unit digit of
125
8
1471
1258
1471
from the unit digit of
125
3
1469
1253
1469
:
3
−
2
=
1
3−2=1
So, the unit digit of the expression
125
3
1469
−
125
8
1471
1253
1469
−1258
1471
is 1.
Therefore, the correct answer is option A. 1.
Verified answer
Answer- B. (9) Here's the answer of your question.