Mathematics

Problem

Let

E = \frac{(27)^{\frac{2}{3}}}{3^{\frac{1}{3}}},\qquad F=(81)^{-\frac{3}{4}}

Answer the following. a. (i) Express the numerator and the denominator of

E

in radical form and hence simplify

E

to a single power of

3

. No decimal approximation is required. b. (ii) Evaluate

F

in its simplest fractional form. c. (iii) Using the results of parts (i) and (ii), find the exact value of

E+F