Breath Math

1. Find:

(i) 64^1/2

(ii)32^1/5

(iii) 125^1/3

Solution:

(i) 64^1/2 = (8²)^1/2 = 8^2*(1/2) = 8

(ii)32^1/5 = (2⁵)^1/5= 2^5*(1/5) = 2

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

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2. Find

(i)9^3/2

(ii) 32^2/5

(iii) 16^3/4   

(iv) 125^-1/3

Solution:

(i)9^3/2 = (9^1/2)³ = 3³ = 9

(ii) 32^2/5 = (32^1/5)² = 2²  = 4

(iii) 16^3/4 = (16^1/4)³ = (2)³ = 8

(iv) 125^-1/3 = (125^1/3)^-1 = 5^-1 = ¹/₅

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3. 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  = 2^{2/3 + 1/5} = 2^10+3/15  = 2^13/15

(ii) (¹/₃³)⁷ = (3^-3)⁷ = 3^-21

(iii) 11^1/2/11^1/4 = 11^{1/2 – 1/4} = 11^2-1/4 = 11^1/4

(iv)7^1/2. 8^1/2 = 56^1/2

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