Problem: The expression (81)−(2−2)(81)^{-\left(2^{-2}\right)}(81)−(2−2) has the same value as:
Answer Choices:
A. 181\dfrac{1}{81}811
B. 13\dfrac{1}{3}31
C. 333
D. 818181
E. 81481^{4}814 Solution:
81−(2−2)=81−1/4=1811/4=1381^{-\left(2^{-2}\right)}=81^{-1 / 4}=\dfrac{1}{81^{1 / 4}}=\dfrac{1}{3}81−(2−2)=81−1/4=811/41=31. Query: Is there another permissible value not listed in the five choices?