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

Problem

(1/4)5/2

Solution

1. Apply the power of a quotient rule by distributing the exponent to both the numerator and the denominator.

(1/4)5/2=1/4

2. Simplify the numerator because 1 raised to any power is 1.

1=1

3. Rewrite the denominator using the definition of rational exponents, where am/n=(√(n,a))m

4=(√(,4))5

4. Evaluate the square root of 4.

√(,4)=2

5. Raise the result to the power of 5.

2=32

6. Combine the results into the final fraction.

1/32

Final Answer

(1/4)5/2=1/32

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