Question:
$\left(\frac{-1}{5}\right)^{3} \div\left(\frac{-1}{5}\right)^{8}$ is equal to
(a) $\left(-\frac{1}{5}\right)^{5}$
(b) $\left(-\frac{1}{5}\right)^{11}$
(c) $(-5)^{5}$
(c) $(-5)^{5}$
Solution:
(c) $(-5)^{5}$
we have:
$\left(\frac{-1}{5}\right)^{3} \div\left(\frac{-1}{5}\right)^{8}=\left(\frac{-1}{5}\right)^{3-8}$
$=\left(\frac{-1}{5}\right)^{-5}$
$=\frac{1}{(-1 / 5)^{5}}$
$=\frac{1}{\left((-1)^{5} / 5^{5}\right)}$
$=\frac{5^{5}}{(-1)^{5}}$
$=\left(\frac{5}{-1}\right)^{5}$
$=(-5)^{5}$