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# Mathematics – Class 9 – Chapter 1- Number Systems – Exercise 1.6 – NCERT Exercise Solution

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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