Evaluate sixth root of 27

Problem

√(6,27)

Solution

1. Rewrite the expression using a fractional exponent.

√(6,27)=27^(1/6)

2. Express the base as a power of a prime number, noting that 27=3^3

27^(1/6)=(3^3)^(1/6)

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

(3^3)^(1/6)=3^(3⋅1/6)

4. Simplify the exponent by multiplying the fractions.

3^(3/6)=3^(1/2)

5. Convert the expression back into radical form.

3^(1/2)=√(,3)

Final Answer

√(6,27)=√(,3)

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