Evaluate (1/25)^(-3/2)

Problem

(1/25)(−3/2)

Solution

1. Apply the negative exponent rule by taking the reciprocal of the base to change the sign of the exponent.

(1/25)(−3/2)=25

2. Rewrite the rational exponent using the property am/n=(√(n,a))m

25=(√(,25))3

3. Evaluate the square root of the base.

√(,25)=5

4. Calculate the power by cubing the result.

5=125

Final Answer

(1/25)(−3/2)=125

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