Exercise 1.6 Page: 26
1. Find:
(i)641/2
Solution:
641/2 = (8×8)1/2
= (82)½
= 81 [⸪2×1/2 = 2/2 =1]
= 8
(ii)321/5
Solution:
321/5 = (25)1/5
= (25)⅕
= 21 [⸪5×1/5 = 1]
= 2
(iii)1251/3
Solution:
(125)1/3 = (5×5×5)1/3
= (53)⅓
= 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
125-1/3 = (5×5×5)-1/3
= (53)-1⁄3
= 5-1 [3×-1/3 = -1]
= 1/5
3. Simplify:
(i) 22/3×21/5
Solution:
22/3×21/5 = 2(2/3)+(1/5) [Since, am×an=am+n____ Laws of exponents]
= 213/15 [⸪2/3 + 1/5 = (2×5+3×1)/(3×5) = 13/15]
(ii) (1/33)7
Solution:
(1/33)7 = (3-3)7 [Since,(am)n = am x n____ Laws of exponents]
= 3-21
(iii) 111/2/111/4
Solution:
111/2/111/4 = 11(1/2)-(1/4)
= 111/4 [(1/2) – (1/4) = (1×4-2×1)/(2×4) = 4-2)/8 = 2/8 = ¼ ]
(iv) 71/2×81/2
Solution:
71/2×81/2 = (7×8)1/2 [Since, (am×bm = (a×b)m ____ Laws of exponents
= 561/2