Evaluate (3/2)^-2

Problem

(3/2)^(−2)

Solution

1. Apply the negative exponent rule, which states that a^(−n)=1/(a^n) For a fraction, this means taking the reciprocal of the base and changing the sign of the exponent.

(3/2)^(−2)=(2/3)^2

2. Apply the power of a quotient rule, which states that (a/b)^n=(a^n)/(b^n)

(2/3)^2=2^2/3^2

3. Evaluate the squares in the numerator and the denominator.

2^2/3^2=4/9

Final Answer

(3/2)^(−2)=4/9

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