Problem: (14)−14=\left(\dfrac{1}{4}\right)^{-\dfrac{1}{4}}=(41​)−41​=
Answer Choices:
A. −16-16−16
B. −2-\sqrt{2}−2​
C. −116-\dfrac{1}{16}−161​
D. 1256\dfrac{1}{256}2561​
E. 2\sqrt{2}2​
Solution:
(14)−14=(122)−14=(2−2)−14=224=212=2\binom{1}{4}^{-\dfrac{1}{4}}=\binom{1}{2^{2}}^{-\dfrac{1}{4}}=\left(2^{-2}\right)^{-\dfrac{1}{4}}=2^{\dfrac{2}{4}}=2^{\dfrac{1}{2}}=\sqrt{2}(41​)−41​=(221​)−41​=(2−2)−41​=242​=221​=2​.