Simplify cube root of x^18

Problem

√(3,x18)

Solution

1. Rewrite the radical expression using a fractional exponent. The rule for converting a radical to an exponent is √(n,am)=am/n

√(3,x18)=(x18)1/3

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

(x18)1/3=x(18⋅1/3)

3. Simplify the exponent by performing the multiplication.

18⋅1/3=6

Final Answer

√(3,x18)=x6

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