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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?
Sabrina
answered
14 years ago
14 years ago
Explain Bot
answered
11 months ago
11 months ago
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.