Problem:
Simplify
3x3x3xx​​​​
Answer Choices:
A. x​
B. 3x2​
C. 27x2​
D. 54x​
E. 81x80​
Solution:
We have
3x3x3xx​​​​​=(x(x(x⋅x21​)31​)31​)31​=(x(x(x23​)31​)31​)31​=(x(x⋅x21​)31​)31​=(x(x23​)31​)31​=(x⋅x21​)31​=(x23​)31​=x21​=x​.​
Answer: A​.
The problems on this page are the property of the MAA's American Mathematics Competitions