Question

Mark (✓) against the correct answer
${\left(\frac{2}{3}\right)}^{-5}=?$

(a) $\frac{32}{243}$
(b) $\frac{243}{32}$
(c) $\frac{-32}{243}$
(d) $\frac{-243}{32}$

Answer 1

(b) $\frac{243}{32}$

${\left(\frac{2}{3}\right)}^{-5}={\left(\frac{3}{2}\right)}^5$ $\left[s\mathrm{ince}{\left(\frac{a}{b}\right)}^{-n}={\left(\frac{b}{a}\right)}^n\right]$

= $\frac{3^5}{2^5}=\frac{3\times 3\times 3\times 3\times 3}{2\times 2\times 2\times 2\times 2}=\frac{243}{32}$