Simplify: i) 2^2/3. 2^1/5    ii) (1/3³)⁷    iii) 11^1/2/11^1/4    iv) 7^1/2. 8^1/2

Solution:

i) 2^2/3.2^1/5

Using exponent rules:  a^p × a^q = a^{p + q}  (For a > 0, where p and q are rational numbers)

= 2^{2/3 + 1/5}

= 2^{(10+3) /15}

= 2^13/15

ii) (1/3³)⁷

Using exponent rules: (a^p)^q = a^pq and 1/a^-n = aⁿ 

(1/3³)⁷ = 1⁷/ (3³)⁷

= 1/3²¹ 

= 3^-21 

iii) 11^1/2/11^1/4

Using exponent rules: a^p/a^q = a^{p - q} 

11^1/2/11^1/4 = 11^{1/2 - 1/4}

= 11^1/4

iv) 7^1/2. 8^1/2

Using exponent rules: a^p.b^p = (a.b)^p 

7^1/2. 8^1/2 = (7 × 8)^1/2 

= 56^1/2

☛ Check: CBSE NCERT Solutions for Class 9 Maths Chapter 1 Number Systems

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Video Solution:

Simplify:
i) 2²/³. 2¹/⁵   ii) (1/3³)⁷    iii) 11¹/² / 11¹/⁴   iv) 7¹/². 8¹/²

NCERT Solutions Class 9 Maths Chapter 1 Exercise 1.6 Question 3:

Summary:

The simplified values of 2^2/3. 2^1/5, (1/3³)⁷, 11^1/2/11^1/4, and 7^1/2. 8^1/2 are 2^13/15, 3^-21, 11^1/4 and 56^1/2 respectively.

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