Evaluate 27^(-2/3)

Problem

27(−2/3)

Solution

1. Apply the negative exponent rule by rewriting the expression as the reciprocal with a positive exponent.

27(−2/3)=1/(27(2/3))

2. Interpret the rational exponent using the rule a(m/n)=(√(n,a))m which means taking the cube root of the base and then squaring the result.

1/(27(2/3))=1/((√(3,27))2)

3. Evaluate the cube root of 27, which is 3 because 3×3×3=27

1/((√(3,27))2)=1/3

4. Square the result in the denominator to find the final value.

1/3=1/9

Final Answer

27(−2/3)=1/9

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