Evaluate (2/5)^-3

Problem

(2/5)(−3)

Solution

1. Apply the negative exponent rule, which states that a(−n)=1/(an) or (a/b)(−n)=(b/a)n

(2/5)(−3)=(5/2)3

2. Distribute the exponent to both the numerator and the denominator using the power of a quotient rule.

(5/2)3=5/2

3. Evaluate the powers in the numerator and denominator.

5=125

2=8

4. Combine the results into a single fraction.

125/8

Final Answer

(2/5)(−3)=125/8

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