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

1 Answer
Apr 17, 2016

= 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)