To multiply and simplify the expression ∛(y^13) ∛(16y^14), you don't add the exponents and multiply the little 3's.
To simplify expressions with radicals, you need to use the rules of exponents and simplify each radical separately before multiplying.
Let's simplify each radical:
∛(y^13) = y^(13/3)
∛(16y^14) = (16y^14)^(1/3)
= 16^(1/3) * (y^14)^(1/3)
= 2 * y^(14/3)
Now, let's multiply the simplified radicals:
y^(13/3) * 2 * y^(14/3) = 2y^(13/3 + 14/3)
To add the exponents, we keep the same base (y) and add the exponents:
2y^(13/3 + 14/3) = 2y^(27/3)
= 2y^9
So, the simplified expression is 2y^9.