Question

Find the value of 7/(512)^-2/3 + 1/(1296)^-3/4 +2/(7776)^-1/5
1. 376
2. 476
3. 576
4. 676

Answer 1

Correct Answer - Option 4 : 676

Formula Used∶

1/a^-m = a^m, (a^m)ⁿ = a^{m × n}

Calculation∶

7/ (512)^-2/3 + 1/ (1296)^-3/4 + 2/ (7776)^-1/5

= 7 × (512)^2/3 + 1 × (1296)^3/4 + 2 × (7776)^1/5

= 7 × (8³)^2/3 + 1 × (6⁴)^3/4 + 2 × (6⁵)^1/5

= 7 × 8^{3 × (2/3)} + 1 × 6^{4 × (3/4)} + 2 × 6^{5 × 1/5}

= 7 × 8² + 1 × 6³ + 2 × 6

= 7 × 64 + 1 × 216 + 2 × 6

= 448 + 216 + 12

= 676.

∴ The required value is 676.