First, we eliminate the negative exponent by switching the numerator and denominator.
[tex] (3x^4)^-2 = \frac{1}{(3x^4)^2} [/tex]
Which then becomes:
[tex] \frac{1}{9x^8} [/tex]
Now we can multiply/combine like terms.
[tex] (\frac{x^{4}y^{11} }{9x^{8}y^{5}} )( \frac{x^{2}y^{5}}{y^2})^2 ( \frac{1}{9x^8} ) \\ = (\frac{x^{4}y^{11} }{9x^{8}y^{5}} )( \frac{x^{4}y^{10}}{y^4}) ( \frac{1}{9x^8} ) \\ =
(\frac{x^{8}y^{21} }{81x^{16}y^{9}} )
[/tex]
Which then simplifies to:
[tex] \frac{y^{12} }{81x^{8}}[/tex]
:)
