Evaluate (8/27)^(-2/3)

Problem

(8/27)(−2/3)

Solution

1. Apply the negative exponent rule by taking the reciprocal of the fraction to change the sign of the exponent.

(8/27)(−2/3)=(27/8)2/3

2. Apply the power of a quotient rule to distribute the exponent to both the numerator and the denominator.

(27/8)2/3=27/8

3. Rewrite the rational exponents as radicals, specifically the square of the cube root of each number.

27/8=((√(3,27))2)/((√(3,8))2)

4. Evaluate the cube roots in the numerator and denominator.

((√(3,27))2)/((√(3,8))2)=3/2

5. Square the results to find the final value.

3/2=9/4

Final Answer

(8/27)(−2/3)=9/4

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