ziyuen wrote:
What is the units digit of \((71)^{5}*(46)^{3}*(103)^{4} + (57)*(1088)^{3}\) ?
A. 0
B. 1
C. 2
D. 3
E. 4
We need to determine the units digit of (71)^5 x (46)^3 x (103)^4 + (57) x (1088)^3. Since we only care about the units digits, we can rewrite the expression as:
What is the units digit of (1)^5 x (6)^3 x (3)^4 + (7) x (8)^3 ?
Since 1 raised to any power always has a units digit of 1, 1^5 will have a units digit of 1.
Since 6 raised to any power always has a units digit of 6, 6^3 will have a units digit of 6.
Since (3)^4 = 81, 3^4 has a units digit of 1.
7, of course, has a units digit of 7.
Since 8^3 = 512, 8^3 has a units digit of 2.
Let’s now plug all of this information into the expression:
1 x 6 x 1 + 7 x 2 = 6 + 14 = 20
Thus, the units digit is 0.
Answer: A
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