I am really stuck, can someone please help me with this?
Multiply and simplify by factoring. Assume that all expressions under radcals represent nonnegative numbers. (type in radical form)
∛(y^13 ) ∛(16y^14 )
I need help with almost the same exact stuff your doing are you in algebra 2
To multiply and simplify by factoring, we need to first factor the expressions under the cube roots. Let's break down each expression:
∛(y^13) can be written as ∛(y^12 * y) since 12 is the largest perfect cube that can be divided from 13.
Similarly, ∛(16y^14) can be written as ∛(2 * 8 * y^12 * y^2) since 8 is the largest perfect cube that can be divided from 16 and y^12 is the largest perfect cube that can be divided from y^14.
Now, let's simplify each of the factors:
∛(y^12 * y) = ∛y^12 * ∛y = y^4 * ∛y (using the property that ∛(ab) = ∛a * ∛b)
∛(2 * 8 * y^12 * y^2) = ∛2 * ∛8 * ∛y^12 * ∛y^2 = 2 * 2 * y^4 * y^(2/3) = 4y^4 * y^(2/3) = 4y^4 * y^(2/3) = 4y^(4 + 2/3) = 4y^(10/3)
Now, let's multiply the simplified expressions:
(y^4 * ∛y) * (4y^(10/3))
To multiply the variables, we add the exponents:
y^4 * y^(10/3) = y^(4 + 10/3) = y^(22/3)
So the final answer is:
4y^(22/3)