Q1: Find the value of:
(ज्ञात कीजिए:)

(i) 64^1/2
We know 64 = 8². So, (8²)^1/2 = 8^{2 × (1/2)} = 8

(ii) 32^1/5
We know 32 = 2⁵. So, (2⁵)^1/5 = 2^{5 × (1/5)} = 2

(iii) 125^1/3
We know 125 = 5³. So, (5³)^1/3 = 5^{3 × (1/3)} = 5

Q2: Find the value of:
(ज्ञात कीजिए:)

(i) 9^3/2
= (3²)^3/2 = 3^{2 × (3/2)} = 3³ = 27

(ii) 16^3/4
= (2⁴)^3/4 = 2^{4 × (3/4)} = 2³ = 8

(iii) 125^-1/3
= (5³)^-1/3 = 5^-1 = 1/5

Q3: Simplify:
(सरल कीजिए:)

(i) 2^2/3 · 2^1/5
Bases are the same, so add exponents: 2/3 + 1/5 = (10 + 3)/15 = 13/15.
= 2^13/15

(ii) 11^1/2 / 11^1/4
Bases are the same in division, so subtract exponents: 1/2 - 1/4 = 1/4.
= 11^1/4

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