Question

Mark (✓) against the correct answer

${\left(\frac{-1}{2}\right)}^{-6}=?$

(a) −64
(b) 64
(c) $\frac{1}{64}$
(d) $\frac{-1}{64}$

Answer 1

(b) 64
We have:
${\left(\frac{-1}{2}\right)}^{-6}={\left(\frac{2}{-1}\right)}^6$ $\left[s\mathrm{ince}{\left(\frac{a}{b}\right)}^{-n}={\left(\frac{b}{a}\right)}^n\right]$
$$\begin{gathered} ={\left(-2\right)}^6 \\ =\left(-2\right)\times \left(-2\right)\times \left(-2\right)\times \left(-2\right)\times \left(-2\right)\times \left(-2\right) \\ =64 \end{gathered}$$