Simplify ((216)^{-frac{2}{3}} times (0.16)^{-frac{3}{2}})
-
A.
(frac{125}{288}) -
B.
(frac{2}{125}) -
C.
(frac{4}{225}) -
D.
(frac{2}{225})
Correct Answer: Option A
Explanation
((216)^{-frac{2}{3}} = (frac{1}{216})^{frac{2}{3}} = (sqrt[3]{frac{1}{216}})^{2} = (frac{1}{6})^{2} = frac{1}{36})
((0.16)^{-frac{3}{2}} = (frac{100}{16})^{frac{3}{2}} = (sqrt{100}{16})^{3} = frac{1000}{64})
(frac{1}{36} times frac{1000}{64} = frac{125}{288})