Evaluate 27^(-1/3)

Problem

27(−1/3)

Solution

1. Apply the negative exponent rule by rewriting the expression as the reciprocal with a positive exponent using the property a(−n)=1/(an)

27(−1/3)=1/(27(1/3))

2. Interpret the rational exponent as a radical using the property a(1/n)=√(n,a) which means the exponent 1/3 represents a cube root.

1/(27(1/3))=1/√(3,27)

3. Evaluate the cube root by identifying the number that, when multiplied by itself three times, equals 27 Since 3×3×3=27 the cube root is 3

1/√(3,27)=1/3

Final Answer

27(−1/3)=1/3

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