Find: i) 64^1/2  ii) 32^1/5  iii) 125^1/3

Solution:

Let's use the concept of exponents and laws of exponents to solve the following.

i) 64^1/2

64^1/2 = (8²) ^1/2 [Since, 64 = 8²]

= 8^{2 × 1/2}  [ Using (a^p)^q = a^pq, where a > 0, p and q are rational numbers]

= 8¹ 

= 8

ii) 32^1/5

32^1/5 = (2⁵)^1/5  [Since, 32 = 2⁵]

= (2)^5 × 1/5 [ Using (a^p)^q = a^pq]

= 2¹

= 2

iii) 125^1/3 = (5³) ^1/3 [Since, 125 = 5³]

= (5)^{3 × 1/3} [ Using (a^p)^q = a^pq]

= 5¹

= 5

☛ Check: Class 9 Maths NCERT Solutions Chapter 1

Video Solution:

Find: i) 64¹/²  ii) 32¹/⁵  iii) 125¹/³

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

Summary:

Hence, the values of 64^1/2, 32^1/5, and 125^1/3 are 8, 2, and 5 respectively.

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