Question

Tick (✓) the correct answer
${\left[{\left\{{\left(-\frac{1}{2}\right)}^2\right\}}^{-2}\right]}^{-1}=?$
(a) $\frac{1}{16}$
(b) 16
(c) $-\frac{1}{16}$
(d) −16

Answer 1

(a) $\frac{1}{16}$

$$\begin{gathered} {\left[{\left\{{\left(-\frac{1}{2}\right)}^2\right\}}^{-2}\right]}^{-1} \\ ={\left[{\left\{-\frac{1}{2}\right\}}^{-4}\right]}^{-1} \\ ={\left(-\frac{1}{2}\right)}^{(-4\times -1)} \\ ={\left(-\frac{1}{2}\right)}^4 \\ =\frac{1}{16} \end{gathered}$$