1. Find:
(i)64 1/2
Solution:
= 64 1/2 = (8×8) 1/2
= (82)1/2
= 81 [2×1/2 = 2/2 =1]
= 8
(ii)32 1/5
Solution:
= 32 1/5 = (25)1/5
= (25) 1/5
= 21 [5×1/5 = 1]
= 2
(iii)125 1/3
Solution:
= (125) 1/3 = (5×5×5)1/3
= (53)1/3
= 51 (3×1/3 = 3/3 = 1)
= 5
2. Find:
(i) 93/2
Solution:
=93/2 = (3×3)3/2
= (32)3/2
= 33 [2×3/2 = 3]
=27
(ii) 322/5
Solution:
=322/5 = (2×2×2×2×2)2/5
= (25)2⁄5
= 22 [5×2/5= 2]
= 4
(iii)163/4
Solution:
= 163/4 = (2×2×2×2)3/4
= (24)3⁄4
= 23 [4×3/4 = 3]
= 8
(iv) 125 (-1/3)
Solution:
= 125 -1/3 = (5×5×5) -1/3
= (53) -1⁄3
= 5-1 [3×-1/3 = -1]
= 1/5
3. Simplify:
(i) 2 2/3 × 2 1/5
Solution:
= 2 2/3 × 2 1/5 = 2 (2/3)+(1/5) [am × an =a m+n]
[Here, 2/3 + 1/5 = (2×5+3×1)/(3×5) = 13/15]
= 213/15
(ii) (1/33)7
Solution:
= (1/33)7 = (3 -3)7
= 3 -21
(iii) 11 1/2/11 1/4
Solution:
= 11 1/2/11 1/4
= 11 (1/2)-(1/4)
[(1/2) – (1/4) = (1×4-2×1)/(2×4) = 4-2)/8 = 2/8 = ¼ ]
= 11 1/4
(iv) 7 ½ × 8 1/2
Solution:
7 ½ × 8 1/2
= (7×8) 1/2
= 56 1/2
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