Reciprocal of \((\frac{-5}{9})^{99}\) is …………….. A) 5/9B)

1.	Reciprocal of \((\frac{-5}{9})^{99}\) is …………….. A) 5/9B) 9/5C) 999 D) None
Answer» Correct option is (D) None Reciprocal of \((\frac{-5}{9})^{99}=\frac1{(\frac{-5}{9})^{99}}=\left[(\frac{-5}{9})^{99}\right]^{-1}\) \(=[-\frac{5}{9}]^{-99}=\left[(\frac{-5}{9})^{-1}\right]^{99}\) \(=(\frac{-9}5)^{99}=(-1)^{99}(\frac95)^{99}\) \(=-\left(\frac{9}5\right)^{99}\) Correct option is D) None

Reciprocal of \((\frac{-5}{9})^{99}\) is …………….. A) 5/9B) 9/5C) 999 D) None

Answer»

Correct option is (D) None

Reciprocal of \((\frac{-5}{9})^{99}=\frac1{(\frac{-5}{9})^{99}}=\left[(\frac{-5}{9})^{99}\right]^{-1}\)

\(=[-\frac{5}{9}]^{-99}=\left[(\frac{-5}{9})^{-1}\right]^{99}\)

\(=(\frac{-9}5)^{99}=(-1)^{99}(\frac95)^{99}\) \(=-\left(\frac{9}5\right)^{99}\)

Correct option is D) None