Question

Mark (✓) against the correct answer
${\left(\frac{-3}{4}\right)}^{-3}=?$

(a) $\frac{27}{64}$
(b) $\frac{64}{27}$
(c) $\frac{-27}{64}$
(d) $\frac{-64}{27}$

Answer 1

(d) $\frac{-64}{27}$

${\left(\frac{-3}{4}\right)}^{-3}={\left(\frac{4}{-3}\right)}^3$ $\left[s\mathrm{ince}{\left(\frac{a}{b}\right)}^{-n}={\left(\frac{b}{a}\right)}^n\right]$

= $\frac{4^3}{{\left(-3\right)}^3}$

= $\frac{4\times 4\times 4}{\left(-3\right)\times \left(-3\right)\times \left(-3\right)}=\frac{64}{\left(-27\right)}$

= $\frac{64\times -1}{-27\times -1}=\frac{-64}{27}$