Given that (a^{frac{5}{6}} times a^{frac{-1}{n}} = 1), solve for n.

Given that (a^{frac{5}{6}} times a^{frac{-1}{n}} = 1), solve for n.

Correct Answer: Option D

Explanation

(a^{frac{5}{6}} times a^{frac{-1}{n}} = 1)

(implies a^{frac{5}{6} + frac{-1}{n}} = a^{0})

Equating bases, we have

(frac{5}{6} – frac{1}{n} = 0)

(frac{5n – 6}{6n} = 0)

(5n – 6 = 0 implies 5n = 6)

(n = frac{6}{5} = 1.20)