Question #6450750Fill in the Blank
Algebra-2
Question
Simplify the expression (). The simplified form is ___________.
Answer & Analysis
Analysis
Question Analysis
This problem assesses the student's ability to simplify a division of radical expressions with higher indices and variables.
This problem assesses the student's ability to simplify a division of radical expressions with higher indices and variables.
Key Concept Explanation
When dividing two radicals with the same index, the quotient of the radicands becomes the new radicand. The coefficients are also divided. The result can be further simplified if possible.
When dividing two radicals with the same index, the quotient of the radicands becomes the new radicand. The coefficients are also divided. The result can be further simplified if possible.
Step-by-step Solution
1. Confirm conditions: Index = 4 (even); radicands 128z⁴ ≥ 0, 2z > 0; same index.
2. Separate coefficients and radicals: .
3. Simplify the radicand:
1. Confirm conditions: Index = 4 (even); radicands 128z⁴ ≥ 0, 2z > 0; same index.
2. Separate coefficients and radicals: .
3. Simplify the radicand:
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