Question

Simplify:

[(32)^2/5 +(9)^3/2 - (125)^-1/3]/[2^2/3 × 2^1/3] 

1. 7/5
2. 5/7
3. 77/5
4. 23/5

Answer 1

Correct Answer - Option 3 : 77/5

Formula Used:

a^-1 = 1/a

a¹ = a

a^m/aⁿ = a^{m - n}

(a^m)ⁿ = a^mn

a^m × aⁿ = a^{m + n}

Calculation:

[(32)2/5 +(9)3/2 - (125)-1/3]/[22/3 × 21/3] 

⇒ [(2)^{2/5 × 5} + (3)^{3/2 × 2} - (5)^{3 × -1/3}]/[ 2^{2/3 + 1/3}]

⇒ [(2)² + (3)3  - (5)-1]/[ 23/3]

⇒ [4 + 27 - 1/5]/2

⇒ (154/5) × 1/2

⇒ 77/5

∴ [(32)2/5 +(9)3/2 - (125)-1/3]/[22/3 × 21/3] = 77/5

The correct option is 3 i.e. 77/5