Question

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

Answer 1

`= 1/(9x^6)`

Explanation:

Use the power rule :
`(x^a)^b = x^{a times b}`
-

So in this case we have
`(-3x^3)^{-2}`
Thus, we need to distribute the -2 exponent to the terms in the parenthesis:
`-3^{-2} times x^{3 times -2}`

Since -3 is raised to a negative power, we need to do:
`1/{-3^{2})`
The same thing needs to be done with `x^{-6}` to make it into a positive exponent:
`1/x^6`

We now have
`1/{-3^{2}) times 1/x^{6}`

Note that since -3 is raised to a power that is of even number, the product will eventually be positive (`-3 times -3 = 9`). So we can take out the negative sign to get:

`1/{3^{2}) times 1/x^{6}`
`= 1/(9x^6)`