Question

How do you simplify `(2/3)^-3`?

Answer 1

`(2/3)^(-3) = 27/8 = 3 3/8`

Explanation:

In general `a^(-b) = 1/(A^b)`

So
`color(white)("XXX")(2/3)^(-3) = 1/((2/3)^3)`

`color(white)("XXXXXXXX")= 1/((2^3)/(3^3))`

`color(white)("XXXXXXXX")= (3^3)/(2^3)`

`color(white)("XXXXXXXX")=27/8`

Answer 2

`27/8`

Explanation:

A negative power is the same thing as the positive power of the inverse number.

So, first of all, `(2/3)^{-3}` is the same thing as `(3/2)^3`.

Now we have to compute the power of a fraction, which is very simple, because it is the power of the numerator divided by the power of the denominator, so

`(3/2)^3 = 3^3 / 2^3 = 27/8`