Find the value of [(2401 a16)/ (1296 b4)]-3/41. (216 a-10 b3)/3432. (3

1.	Find the value of [(2401 a16)/ (1296 b4)]-3/41. (216 a-10 b3)/3432. (343 a-12 b3)/2163. (343 a-12 b2)/2164. (216 a-12 b3)/343
Answer» 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 = [(7⁴a¹⁶)/(6⁴b⁴)]^-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^-12b³)/343 ∴ The required value is 216 a^-12 b³/343.

Find the value of [(2401 a16)/ (1296 b4)]-3/41. (216 a-10 b3)/3432. (343 a-12 b3)/2163. (343 a-12 b2)/2164. (216 a-12 b3)/343

Answer» 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

= [(7⁴a¹⁶)/(6⁴b⁴)]^-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^-12b³)/343

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