Question

Which of the following numbers is not equal to $\frac{-8}{27}$?
(a) $(\frac{2}{3}{)}^{-3}$

(b) $-(\frac{2}{3}{)}^3$

(c) $(-\frac{2}{3}{)}^3$

(d) $\frac{-2}{3}\times \frac{-2}{3}\times \frac{-2}{3}$

Answer 1

The correct option is (a): $(\frac{2}{3}{)}^{-3}$

For option (a)

$(\frac{2}{3}{)}^{-3}=(\frac{3}{2}{)}^3$ [Using the identity $a^{-1}=\frac{1}{a}$]

$=\frac{3}{2}\times \frac{3}{2}\times \frac{3}{2}=\frac{27}{8}$

so, option (a), is not equal to given question i.e, $\frac{-8}{27}$

Check for option (b)

$-(\frac{2}{3}{)}^3=-(\frac{2}{3})\times (\frac{2}{3})\times (\frac{2}{3})=-\frac{8}{27}$

so, option (b) is equal to the given question.

Check for option (c)

$(-\frac{2}{3}{)}^3=(-\frac{2}{3})\times (-\frac{2}{3})\times (-\frac{2}{3})=\frac{-2\times -2\times -2}{3\times 3\times 3}=\frac{-8}{27}$

so, option (c) is equal to the given question.

Check for option (d)

$\frac{-2}{3}\times \frac{-2}{3}\times \frac{-2}{3}=\frac{-2\times -2\times -2}{3\times 3\times 3}=\frac{-8}{27}$

so, option (d) is equal to the given question.

Hence, our answer will be option (a).