Evaluate (-216)^(-2/3)

Problem

(−216)(−2/3)

Solution

1. Apply the negative exponent rule to rewrite the expression as a reciprocal with a positive exponent.

1/((−216)(2/3))

2. Interpret the fractional exponent as a power of a root, where the denominator 3 represents the cube root and the numerator 2 represents the square.

1/((√(3,−216))2)

3. Evaluate the cube root of −216 by finding the number that, when multiplied by itself three times, equals −216

√(3,−216)=−6

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

1/((−6)2)

5. Simplify the denominator by calculating the square of −6

(−6)2=36

Final Answer

(−216)(−2/3)=1/36

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