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Question
The multiplicative inverse of `(- 5/9)^99` is ______.
Options
`(-5/9)^99`
`(5/9)^99`
`(9/(-5))^99`
`(9/5)^99`
Solution
The multiplicative inverse of `(- 5/9)^99` is `underlinebb((-5/9)^99)`.
Explanation:
For multiplicative inverse, a is called multiplicative inverse of b, if a × b = 1.
Put `b = ((-5)/9)^-99`
⇒ `a xx ((-5)/9)^-99 = 1`
⇒ `a = 1/((-5)/9)^-99` ...`[∵ a^-m = 1/a^m]`
⇒ `a = (- 5/9)^99`
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