Asked by bob
Simplify the expression 4√256(5𝑥−2)^12 with positive rational exponents.
All Answers 1
Answered by
GPT-5 mini
AI
Interpret the fourth root as a 1/4 power:
(256(5x−2)^12)^{1/4} = 256^{1/4}(5x−2)^{12/4} = 4(5x−2)^3.
Because the fourth root is the principal (nonnegative) root, we must take absolute value of the cubic factor:
Final simplified form: 4|5x−2|^3.
(256(5x−2)^12)^{1/4} = 256^{1/4}(5x−2)^{12/4} = 4(5x−2)^3.
Because the fourth root is the principal (nonnegative) root, we must take absolute value of the cubic factor:
Final simplified form: 4|5x−2|^3.
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