Question

Mark (✓) against the correct answer
$\left\{{\left(\frac{1}{3}\right)}^{-3}-{\left(\frac{1}{2}\right)}^{-3}\right\}=?$

(a) 19
(b) $\frac{1}{19}$
(c) −19
(d) $\frac{-1}{19}$

Answer 1

(a) 19

$\left\{{\left(\frac{1}{3}\right)}^{-3}-{\left(\frac{1}{2}\right)}^{-3}\right\}=\left\{{\left(\frac{3}{1}\right)}^3-{\left(\frac{2}{1}\right)}^3\right\}$ $\left[s\mathrm{ince}{\left(\frac{\mathrm{a}}{\mathrm{b}}\right)}^{-1}={\left(\frac{\mathrm{b}}{\mathrm{a}}\right)}^1\right]$
= $\left\{{\left(3\right)}^3-{\left(2\right)}^3\right\}$
= (27 − 8) = 19