Final answer:
To simplify the given expression, we divide the terms by subtracting the exponents and move the negative exponents to the denominator. The final answer is (1/2)11x7y-1.
Step-by-step explanation:
To simplify the expression, we need to follow the rules of exponentiation. In this case, we have a negative exponent, which means that the corresponding term should be moved to the denominator. So, starting with (2x-2y-6z-1/(4x-9yz-5))-1, we can rewrite it as 1/((2x-2y-6z-1)/(4x-9yz-5)).
Next, we can simplify the expression inside the parentheses by dividing the terms with the same base and subtracting the exponents. So, ((2/4)x(-2-(-9))y(-6-(-5))z(-1-(-1))).
After simplifying, we get (1/2)11x7y-1z0. Finally, since any number raised to the power of 0 is 1 and we want positive exponents, we can remove the z term from the expression, resulting in the final answer: (1/2)11x7y-1.