Solve the following

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:

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

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

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

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

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

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

$=(-5)^{5}$

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