Problem: When simplified (−1125)−2/3\left(-\dfrac{1}{125}\right)^{-2 / 3}(−1251)−2/3 becomes:
Answer Choices:
A. 125\dfrac{1}{25}251
B. −125-\dfrac{1}{25}−251
C. 252525
D. −25-25−25
E. 25−125 \sqrt{-1}25−1 Solution:
(−1125)−2/3=(−125)2/3=((−125)1/2)3=(−5)2=25\left(-\dfrac{1}{125}\right)^{-2 / 3}=(-125)^{2 / 3}=\left((-125)^{1 / 2}\right)^{3}=(-5)^{2}=25(−1251)−2/3=(−125)2/3=((−125)1/2)3=(−5)2=25