Final answer:
The cube root of 162 has been factored into the cube root of 27 and the cube root of 6. The simplest form is thus 3 times the cube root of 6, so a = 3 and b = 6.
Step-by-step explanation:
The student is working on finding the cube root of 162 and has already correctly factored this into the cube root of 27 times the cube root of 6. To simplify this, we recognize that 27 is a perfect cube (3³), so the cube root of 27 is 3. Therefore, the simplest form of ∛162 can be written as:
∛162 = ∛27 × ∛6
This simplifies to:
3 × ∛6
Where the ∛ symbol represents the cube root. As such, in the form ∛a∛b, where 'a' is the cube root of a perfect cube and 'b' is the remaining factor, we have a = 3 and b = 6 for this equation.
162 was factored into a product of 27 (a perfect cube) and 6, which cannot be further simplified in terms of cube roots.