Correct $$ \left(\frac{x^{-1} y^{-3}}{x^{3} y^{-1}}\right)^{2}\left(\frac{x^{-3} y^{-2}}{x^{3} y^{3}}\right)^{3} $$

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Calculate or simplify the expression $$ \left(\frac{x^{-1} y^{-3}}{x^{3} y^{-1}}ight)^{2}\left(\frac{x^{-3} y^{-2}}{x^{3} y^{3}}ight)^{3} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\left(\frac{x^{-1}y^{-3}}{x^{3}y^{-1}}ight)^{2}\left(\frac{x^{-3}y^{-2}}{x^{3}y^{3}}ight)^{3}$$
- step1: Multiply by $$a^{-n}:$$
  $$\left(x^{-1}y^{-3}x^{-3}yight)^{2}\left(\frac{x^{-3}y^{-2}}{x^{3}y^{3}}ight)^{3}$$
- step2: Reduce the fraction:
  $$\left(x^{-1}y^{-3}x^{-3}yight)^{2}\left(\frac{1}{x^{6}y^{5}}ight)^{3}$$
- step3: Multiply:
  $$\left(x^{-4}y^{-2}ight)^{2}\left(\frac{1}{x^{6}y^{5}}ight)^{3}$$
- step4: Evaluate the power:
  $$\left(x^{-4}y^{-2}ight)^{2}\left(x^{6}y^{5}ight)^{-3}$$
- step5: Rewrite the expression:
  $$x^{-8}y^{-4}x^{-18}y^{-15}$$
- step6: Multiply the terms:
  $$x^{-26}y^{-4}	imes y^{-15}$$
- step7: Multiply the terms:
  $$x^{-26}y^{-19}$$
- step8: Simplify:
  $$\frac{1}{x^{26}y^{19}}$$
The simplified form of the expression $$\left(\frac{x^{-1} y^{-3}}{x^{3} y^{-1}}ight)^{2}\left(\frac{x^{-3} y^{-2}}{x^{3} y^{3}}ight)^{3}$$ is $$\frac{1}{x^{26}y^{19}}$$.
The simplified form of the expression is $$ \frac{1}{x^{26}y^{19}} $$.

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