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.

1/((−27)(2/3))

2. Rewrite the rational exponent using the property a(m/n)=(√(n,a))m

1/((√(3,−27))2)

3. Evaluate the cube root of −27 which is the number that, when multiplied by itself three times, equals −27

√(3,−27)=−3

4. Substitute the root back into the expression and square the result.

1/((−3)2)

5. Simplify the denominator by calculating (−3)×(−3)

1/9

Final Answer

(−27)(−2/3)=1/9

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