Question

x = √2 then (x^x)^x = ………………….

A) \(\frac{1}{\sqrt2}\)

B) \(\frac{1}{4\sqrt2}\)

C) \(\frac{1}{3\sqrt2}\)

D) \(\frac{1}{5\sqrt2}\)

Answer 1

Correct option is (B) \(\frac{1}{4\sqrt{2}}\)

\(x=\sqrt{2}=2^\frac12\)

Then \(x^{-5}=\frac1{x^5}=\frac1{(2^\frac12)^5}\) \(=\frac1{2^\frac52}=\frac1{2^{2+\frac12}}\) \(=\frac{1}{2^2.2^\frac12}=\frac{1}{4\sqrt{2}}\)

Answer 2

Correct option is   B) \(\frac{1}{4\sqrt2}\)