Evaluate (3/5)^-3

Problem

(3/5)(−3)

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.

(3/5)(−3)=(5/3)3

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

(5/3)3=5/3

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

5=125

3=27

4. Combine the results into a single fraction.

125/27

Final Answer

(3/5)(−3)=125/27

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