Simplify square root of cube root of 1-x

Problem

√(,√(3,1−x))

Solution

1. Express the radicals as fractional exponents using the rule √(n,a)=a(1/n)

√(,√(3,1−x))=((1−x)(1/3))(1/2)

2. Apply the power of a power rule, which states that (am)n=a(m⋅n)

1/3⋅1/2=1/6

3. Combine the exponents to simplify the expression into a single power.

(1−x)(1/6)

4. Rewrite the expression back into radical form using the rule a(1/n)=√(n,a)

√(6,1−x)

Final Answer

√(,√(3,1−x))=√(6,1−x)

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