Problem: What is the value of
2(0(19))+((20)1)9?2^{(0^{(1^{9})})}+((2^{0})^{1})^{9}? 2(0(19))+((20)1)9?
Answer Choices:
A. 000 B. 111 C. 222 D. 333 E. 444
Solution:
2(0(19))+((20)1)9=2(01)+((1)1)9=20+19=1+1=(C)22^{(0^{(1^{9})})}+((2^{0})^{1})^{9}=2^{(0^{1})}+((1)^{1})^{9}=2^{0}+1^{9}=1+1= \text{(C)}\boxed{2} 2(0(19))+((20)1)9=2(01)+((1)1)9=20+19=1+1=(C)2​
The problems on this page are the property of the MAA's American Mathematics Competitions