Multiply and simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers. ∛(y^13 ) ∛(¡¼16y¡½^14 )
I got ∛16y^27
Am I right?
To multiply and simplify by factoring the given expression ∛(y^13) ∛(16y^14), we can follow these steps:
Step 1: Use the property of radicals that states ∛(a) ∛(b) = ∛(a * b). This allows us to multiply the expressions together.
∛(y^13) ∛(16y^14) = ∛(y^13 * 16y^14)
Step 2: Multiply the coefficients (numbers) and then multiply the variables with the same base.
∛(y^13 * 16y^14) = ∛(16 * y^13 * y^14)
Step 3: Simplify the coefficients and combine the variables.
∛(16 * y^13 * y^14) = ∛(16y^27)
Therefore, the simplified expression is ∛(y^13) ∛(16y^14) = ∛(16y^27).
So, yes, your answer ∛(16y^27) is correct!