Evaluate (1/4)^(-5/2)

Problem

(1/4)(−5/2)

Solution

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

(1/4)(−5/2)=4

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

4=(√(,4))5

3. Evaluate the square root of the base.

√(,4)=2

4. Calculate the power by raising the result to the numerator of the exponent.

2=32

Final Answer

(1/4)(−5/2)=32

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