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.