Final answer:
To simplify the expression root(3)(27a9b12c6), rewrite the number inside the radical as a product of prime factors. Take out the cube roots of the perfect cubes under the radical.
Step-by-step explanation:
To simplify the expression root(3)(27a9b12c6), we need to rewrite the number inside the radical as a product of prime factors. The prime factorization of 27 is 3*3*3, the prime factorization of 9 is 3*3, the prime factorization of 12 is 2*2*3, and the prime factorization of 6 is 2*3. Now, we can rewrite the expression as root(3)(3*3*3*a^9*b^12*c^6). Taking out the cube roots of the perfect cubes under the radical, we have 3*a^3*b^4*c^2*root(3)(abc), which is the simplest form of the expression.