Evaluate 27^(1/3)

Problem

27(1/3)

Solution

1. Identify the meaning of the fractional exponent, where an exponent of 1/3 represents the cube root of the base.

27(1/3)=√(3,27)

2. Rewrite the base as a power of a prime number, noting that 27 is 3 multiplied by itself three times.

27=3

3. Substitute the power back into the expression and apply the power of a power rule, which states (am)n=a(m⋅n)

(3)(1/3)=3(3⋅1/3)

4. Simplify the exponent by multiplying the fractions.

3=3

Final Answer

27(1/3)=3

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