Question

How do you express `(3x^2)^-3` with positive exponents?

Answer 1

`(3x^2)^(-3)=1/(27x^6)`

Explanation:

We can use the identities `a^(-m)=1/a^m`, `(a^m)^n=a^(mn)` and `(ab)^m=a^mb^m`

Hence, `(3x^2)^(-3)`

= `1/(3x^2)^3`

= `1/(3^3*(x^2)^3)`

= `1/(27*x^(2xx3))`

= `1/(27x^6`

Answer 2

`1/(27x^6)`

Explanation:

Method Example:

Suppose we had `t^(-3)`. This is another way of writing `1/(t^3)`

Suppose we had `1/(t^-3)` this is another way of writing `t^3`

So the negative power (index) has the effect of moving the value to the other side of the horizontal line.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Given:`" "(3x^2)^-3`

The index `-3` is acting on everything inside the brackets. So this is the same as:

`1/(3x^2)^3" "->" "1/(3^3xx x^2 xx x^2 xx x^2)" "->" "1/(3^3x^(2xx3))`

`=1/(27x^6)`