Which of the following expressions has the greatest value? · ABC26GN1903
Subject: General Aptitude · Chapter: Surds and Indices
Which of the following expressions has the greatest value?
(a)$\left[\left(2^{-1}\right)^{0}\right]^{2}$
(b)$\left[\left(4^{0}\right)^{-\frac{1}{2}}\right]^{2}$
(c)$\left[\left(2^{-2}\right)^{-1}\right]^{2}$
(d)$\left[\left(2^{-1}\right)^{2}\right]^{2}$
Answer
Explanation
$\left[\left(2^{-1}\right)^{0}\right]^{2}=\left[\left(\frac{1}{2}\right)^{0}\right]^{2}=(1)^{2}=1$. $$\begin{aligned} & {\left[\left(4^{0}\right)^{-\frac{1}{2}}\right]^{2}=\left[(1)^{-\frac{1}{2}}\right]^{2}=(1)^{2}=1 .} \\ & {\left[\left(2^{-2}\right)^{-1}\right]^{2}=\left[\left(\frac{1}{2^{2}}\right)^{-1}\right]^{2}=\left[\left(\frac{1}{4}\right)^{-1}\right]^{2}=(4)^{2}=16 .} \\ & {\left[\left(2^{-1}\right)^{2}\right]^{2}=\left[\left(\frac{1}{2}\right)^{2}\right]^{2}=\left(\frac{1}{4}\right)^{2}=\frac{1}{16} .} \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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