I believe the simplest approach here would be to rewrite (xy^2z)^3 as follows:
x^3 y^6 z^3, and (-9x^2yz)^2 as 81x^4y^2z^2.
Now, multiply x^3 y^6 z^3 * 81x^4y^2z^2.
81x^3x^4 comes out to 81x^7. y^6*4y^2 comes out to 4y^8. Finally, z^3(z^2) comes out to z^5. Now string these 3 products together to obtain your final answer.