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

Answer 1

# = 1/(9x^6)#

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)#

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Answer 2

Jace Anderson

To simplify ((-3x^3)^{-2}), apply the negative exponent to both the base and the exponent inside the parentheses:

((-3x^3)^{-2} = \frac{1}{(-3x^3)^{2}})

Now, simplify the expression inside the parentheses:

((-3x^3)^{2} = (-3)^2(x^3)^2 = 9x^6)

Finally, substitute (9x^6) back into the original expression:

((-3x^3)^{-2} = \frac{1}{9x^6})

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.