Final answer:
To simplify the expression 6√y^3, we recognize that the cube root and cubing are inverse operations. This simplifies directly to 6y, because the radical and the exponent cancel each other out.
Step-by-step explanation:
The student is asking to simplify an expression with a radical, specifically 6√y^3. To simplify this, we can use the rule that allows us to combine exponentiation and radicals. Since the cube root is the same as raising to the power of 1/3, we rewrite y^3 as (y^1)^3. The cube root of y cubed is just y, because (y^1)^3 and √(y^3) are inverse operations. Hence, 6√y^3 simplifies to 6y.
This simplification process involves eliminating terms wherever possible to simplify the algebra, with a final check to see if the result is reasonable. No calculations are needed that would require a calculator with a y* button or techniques for finding fourth roots or cubing exponentials, as suggested in some of the referenced information. However, understanding the relationship between powers and roots is essential to simplifying the expression correctly.