Evaluate (-8)^(-2/3)

Problem

(−8)(−2/3)

Solution

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

1/((−8)(2/3))

2. Rewrite the rational exponent using the property a(m/n)=(√(n,a))m to separate the root and the power.

1/((√(3,−8))2)

3. Evaluate the cube root of −8 which is the number that, when multiplied by itself three times, equals −8

√(3,−8)=−2

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

1/((−2)2)

5. Simplify the denominator by calculating the square of −2

(−2)2=4

Final Answer

(−8)(−2/3)=1/4

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