Question

Find the value of [(2401 a¹⁶)/ (1296 b⁴)]^-3/4
1. (216 a^-10 b³)/343
2. (343 a^-12 b³)/216
3. (343 a^-12 b²)/216
4. (216 a^-12 b³)/343

Answer 1

Correct Answer - Option 4 : (216 a^-12 b³)/343

Formula used∶

(a^m)ⁿ = a^{m + n}, a^-m = 1/a^m, Basic Knowledge of addition of fraction.

Calculation∶

[(2401 a¹⁶)/(1296 b⁴)]^-3/4

= [(7⁴ a¹⁶)/(6⁴ b⁴)]^-3/4

= [7^{4 × (-3/4)}. a^{16 × (-3/4)}]/[6^{4 × (-3/4)}. b^{4 ×(-3/4)}]

= [7^-3. a^-12]/[6^-3. b^-3]

= [6³. b³]/[7³. a¹²]

= 216 b³/ 343 a¹²

= (216 a^-12 b³)/343

∴ The required value is 216 a^-12 b³/343.