Simplify: (i) 23/2 + 21/5 (ii) (1/33)^7 (iii) 11/12 / 11/14 (iv) 7/12 × 8/12

(i) 23/2 + 21/5
By using property Xa.Xb = Xa+b
= 2^(3/2 + 1/5) = 2^(17/10)
(ii) (1/33)^7
By using property (xy)^a = x^a y^a
= 1^(33)^7 = 1/3^21
..[(x^a)^b = x^ab]
(iii) 11/12 / 11/14
By using property X^a/X^b = X^(a-b)
= 11/12 * 14/11 = 14/12 = 7/6
(iv) 7/12 × 8/12 = 56/144 = 7/18
..[x^a y^a = (xy)^a]