Multiply and simplify by factoring. Assumem that all expressions under radicals represent nonnegative numbers.

∛(y^13) ∛(16y^14)

∛y^13 x 16y^14
∛16y^27

Am I even close here?

(been gone all day.)

∛16y^27
= (16y^27)^(1/3)
= 16^(1/3) (y^27)^(1/3)
= 2∛2 y^9

Yes, you're on the right track! Let's go through the steps to verify your answer.

To multiply the two cube roots, ∛(y^13) and ∛(16y^14), we can combine them by multiplying their radicands (the expressions inside the radicals), which in this case are y^13 and 16y^14.

So, the product becomes:

∛(y^13) * ∛(16y^14) = ∛(y^13 * 16y^14)

Next, let's simplify the expression by factoring the term inside the cube root.

First, we can factor out the largest possible perfect cube from y^13 and 16y^14. In this case, we can factor out y^13 from both terms:

∛(y^13 * 16y^14) = ∛(y^13 * y^13 * 16y)

Simplifying further:

∛(y^13 * y^13 * 16y) = ∛(16y^26 * y)

Now, we can simplify the expression inside the cube root. Since we are assuming that all expressions under radicals represent nonnegative numbers, we can rewrite the expression with rational exponents:

∛(16y^26 * y) = (16y^26 * y)^(1/3)

Finally, applying the properties of exponents, we multiply the exponents:

(16y^26 * y)^(1/3) = 16^(1/3) * (y^26 * y)^(1/3)

The cube root of 16 can be simplified as 2 because 2^3 = 8:

16^(1/3) = 2

The cube root of y^27 can be simplified as y^9 because (y^9)^3 = y^27:

(y^26 * y)^(1/3) = y^9

Therefore, the fully simplified expression is:

∛(y^13) * ∛(16y^14) = 2y^9

So, your answer is correct!