Evaluate (-64)^(-2/3)

Problem

(−64)^(−2/3)

Solution

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

1/((−64)^(2/3))

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

1/((√(3,−64))^2)

3. Evaluate the cube root of −64 Since (−4)×(−4)×(−4)=−64 the cube root is −4

1/((−4)^2)

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

1/16

Final Answer

(−64)^(−2/3)=1/16

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