Given that \(a^{\frac{5}{6}} \times a^{\frac{-1}{n}} = 1\), solve for n.
- -6.00
- -1.20
- 0.83
-
1.20
The correct answer is: 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
\(\frac{5}{6} - \frac{1}{n} = 0\)
\(\frac{5n - 6}{6n} = 0\)
\(5n - 6 = 0 \implies 5n = 6\)
\(n = \frac{6}{5} = 1.20\)