Evaluate (2/5)^-3

Problem

(2/5)^(−3)

Solution

1. Apply the negative exponent rule, which states that a^(−n)=1/(a^n) 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=5^3/2^3

3. Evaluate the powers in the numerator and denominator.

5^3=125

2^3=8

4. Combine the results into a single fraction.

125/8

Final Answer

(2/5)^(−3)=125/8

Want more problems? Check here!