Question

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

(b) \[- \left( \frac{2}{3} \right)^3\]

(c) \[\left( - \frac{2}{3} \right)^3\]

(d) \[\left( \frac{- 2}{3} \right) \times \left( \frac{- 2}{3} \right) \times \left( \frac{- 2}{3} \right)\]

Answer 1

(a) \[\left( \frac{2}{3} \right)^{- 3}\]
We can write  `(-8)/27` as `(-2xx(-2)xx(-2))/(3xx3xx3)`. It can be written in the forms given below.

`(-2xx(-2)xx(-2))/(3xx3xx3) = -(2xx2xx2)/(3xx3xx3)` → work out the minuses

`=-2/3xx2/3xx2/3`

`=-(2/3)^3`

Hence, option (b) is equal to `((-8)/27)`

We can also write:

`(-2xx(-2)xx(-2))/(3xx3xx3)=(-2/3)xx(-2/3)xx(-2/3)`

`=-(2/3)^3`

Hence, option (c) is also equal to`(-8)/27`
We can also write:

`(-2xx(-2)xx(-2))/(3xx3xx3) = -(2xx2xx2)/(3xx3xx3)`

Hence, option (d) is also equal to \[- \frac{8}{27}\]
This leaves out option (a) as the one not equal to \[- \frac{8}{27}\]