Question

(-2/3)^3 (Evaluate)

A: 8/9
B: 6/9
C: -8/27
D: 8/27

Answer 1

Power with a natural exponent.

Definition:

`a^2=a\cdot a\\\\a^3=a\cdot a\cdot a\\\\a^4=a\cdot a\cdot a\cdot a\\\vdots\\a^n=\underbrace{a\cdot a\cdot a\cdot...\cdot a}_(n)`

also

`a^1=a\\\\a^0=1`

We have

`\left(-(2)/(3)\right)^3=\left(-(2)/(3)\right)\cdot\left(-(2)/(3)\right)\cdot\left(-(2)/(3)\right)=-(2\cdot2\cdot2)/(3\cdot3\cdot3)=-(8)/(27)`

`\huge\boxed{C:\ -(8)/(27)}`

Answer 2

C

Explanation:

using the rule of exponents

`((a)/(b)) ^(m)` =
`(a^(m) )/(b^(m) )` , then

`((-2)/(3)) ^(3)`

=
`((-2)^(3) )/(3^3)`

=
`(-8)/(27)`

= -
`(8)/(27)`