Multiply and simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers.
∛(y^13 ) ∛(¡¼16y¡½^14 )
Am I supposed to add the exponents and multiply the little 3's?
I could really use help with this problem.
To multiply and simplify the expression ∛(y^13) ∛(16y^14) by factoring, you need to apply the properties of exponents and simplify each cube root separately before multiplying.
Let's break it down step by step:
Step 1: Simplify the cube roots individually.
• ∛(y^13) = ∛(y^(3 * 4 + 1)) = ∛(y^12 * y^1) = ∛(y^12) * ∛(y^1) = y^4 * y^(1/3) = y^(4 + 1/3) = y^(13/3)
• ∛(16y^14) = ∛(16 * y^(3 * 4 + 2)) = ∛(16 * y^12 * y^2) = 2 * y^4 * y^(2/3) = 2y^(4 + 2/3) = 2y^(14/3)
Step 2: Multiply the simplified expressions.
y^(13/3) * 2y^(14/3) = 2y^((13 + 14)/3) = 2y^(27/3) = 2y^9
Therefore, the simplified expression is 2y^9.
Remember, when multiplying expressions with the same base raised to different exponents, you can add the exponents to find the result.