Question

${\left(\frac{-1}{5}\right)}^3÷{\left(\frac{-1}{5}\right)}^8$ is equal to
(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

Correct option is C. $(-5{)}^5$

Given: ${\left(\frac{-1}{5}\right)}^3÷{\left(\frac{-1}{5}\right)}^8$

We know that $a^m÷a^n=a^{m-n}$

$\therefore {\left(\frac{-1}{5}\right)}^3÷{\left(\frac{-1}{5}\right)}^8=(\frac{-1}{5}{)}^{3-8}$

$=(\frac{-1}{5}{)}^{-5}$

$=(-5{)}^5$ [$\because (\frac{a}{b}{)}^{-n}=(\frac{b}{a}{)}^n$]

Hence, ${\left(\frac{-1}{5}\right)}^3÷{\left(\frac{-1}{5}\right)}^8=(-5{)}^5$