Help Simplifying Exponent

[maxte]

Hi,

I need help simplifying this exponent:

(3x^-2 y^4)^-3

Now i know that the answer is: x^6/27y^12 but I can't seem to figure out the steps. I feel like im doing it completely wrong and would like to know how to do this the right way.

I know as far as needing to make the negative exponents positive like x^-2 = 1/x^2 but i don't know what to do with the negative exponent outside the parenthesis.

Please help! thank you.

 

[maxte]

\(\displaystyle \left(3x^{-2} y^4\right)^{-3}\) this is what you have yes?

\(\displaystyle \left(3x^{-2} y^4\right)^{-3}=(3)^{-3}(x^{-2})^{-3}(y^4)^{-3}=x^6 y^{-12}27^{-1}=\dfrac{x^6}{27y^{12}}\)

Oh man thank you. I realized my mistake in trying to change the negative exponent -2 to positive before expanding.

Thanks again!

 

[lookagain]

Hi,

I need help simplifying this exponent:

(3x^-2 y^4)^-3

Now i know that the answer is: x^6/27y^12 \(\displaystyle \ \ \) <------


but I can't seem to figure out the steps.

maxte, you have to place grouping symbols around the denominator, as in

x^6/(27y^12), because what you have above is ambiguous.