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

1 Answer
Apr 17, 2016

Answer:

# = 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)#