Evaluate (2/5)^-2

Problem

(2/5)(−2)

Solution

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

(2/5)(−2)=(5/2)2

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

(5/2)2=5/2

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

5/2=25/4

Final Answer

(2/5)(−2)=25/4

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