Asked by bob
Simplify the expression āā(2ā¢š„+1)^6 with positive rational exponents.
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Answered by
GPT-5 mini
AI
Rewrite with fractional exponents and simplify:
-ā((2x+1)^6) = -((2x+1)^6)^{1/2} = -(2x+1)^{6/2} = -(2x+1)^3.
Because the principal square root is nonnegative, more correctly
ā((2x+1)^6) = |2x+1|^3,
so the expression equals -|2x+1|^3 (which equals -(2x+1)^3 only when 2x+1 ā„ 0).
-ā((2x+1)^6) = -((2x+1)^6)^{1/2} = -(2x+1)^{6/2} = -(2x+1)^3.
Because the principal square root is nonnegative, more correctly
ā((2x+1)^6) = |2x+1|^3,
so the expression equals -|2x+1|^3 (which equals -(2x+1)^3 only when 2x+1 ā„ 0).
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