If x = 64 and y = 27, evaluate: (frac{x^{frac{1}{2}} – y^{frac{1}{3}}}{y – x^{frac{2}{3}}})
-
A.
2(frac{1}{5}) -
B.
1 -
C.
(frac{5}{11}) -
D.
(frac{11}{43})
Correct Answer: Option C
Explanation
(frac{x^{frac{1}{2}} – y^{frac{1}{3}}}{y – x^{frac{2}{3}}})
substitute x = 64 and y = 27
(frac{64^{frac{1}{2}} – 27^{frac{1}{3}}}{27 – 64^{frac{2}{3}}} = frac{sqrt{64} – 3sqrt{27}}{27 – (3sqrt{64})^2})
= (frac{8 – 3}{27 – 16})
= (frac{5}{11})