Question

Mark (✓) against the correct answer
${\left(\frac{-2}{5}\right)}^7÷{\left(\frac{-2}{5}\right)}^5=?$

(a) $\frac{4}{25}$
(b) $\frac{-4}{25}$
(c) ${\left(\frac{-2}{5}\right)}^{12}$
(d) $\frac{25}{4}$

Answer 1

(a) $\frac{4}{25}$

${\left(\frac{-2}{5}\right)}^7÷{\left(\frac{-2}{5}\right)}^5={\left(\frac{-2}{5}\right)}^{7-5}$ $\left[s\mathrm{ince}{\mathrm{a}}^{\mathrm{m}}÷{\mathrm{a}}^{\mathrm{n}}={\mathrm{a}}^{\mathrm{m}-\mathrm{n}}\right]$
$={\left(\frac{-2}{5}\right)}^2$
= $\frac{{\left(-2\right)}^2}{{\left(5\right)}^2}=\frac{4}{25}$