Question

Mark (✓) against the correct answer
${\left(\frac{-1}{5}\right)}^3÷{\left(\frac{-1}{5}\right)}^8=?$

(a) ${\left(-\frac{1}{5}\right)}^5$
(b) ${\left(\frac{-1}{5}\right)}^{11}$
(c) (−5)⁵
(d) ${\left(\frac{1}{5}\right)}^5$

Answer 1

(c) (-5)⁵

We have:
${\left(\frac{-1}{5}\right)}^3÷{\left(\frac{-1}{5}\right)}^8={\left(\frac{-1}{5}\right)}^{3-8}$ $\left[s\mathrm{ince}{\mathrm{a}}^{\mathrm{m}}÷{\mathrm{a}}^{\mathrm{n}}={\mathrm{a}}^{\mathrm{m}-\mathrm{n}}\right]$
= ${\left(\frac{-1}{5}\right)}^{-5}$
$={\left(\frac{5}{-1}\right)}^5$ $\left[\mathrm{Since}{\left(\frac{\mathrm{a}}{\mathrm{b}}\right)}^{-1}={\left(\frac{\mathrm{b}}{\mathrm{a}}\right)}^1\right]$
$={\left(\frac{5\times -1}{-1\times -1}\right)}^5={\left(\frac{-5}{1}\right)}^5={\left(-5\right)}^5$