Evaluate (1/9)^(3/2)

Problem

(1/9)(3/2)

Solution

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

(1/9)(3/2)=(1(3/2))/(9(3/2))

2. Simplify the numerator since any positive power of 1 is 1

(1(3/2))/(9(3/2))=1/(9(3/2))

3. Rewrite the fractional exponent in the denominator using the property a(m/n)=(√(n,a))m

1/(9(3/2))=1/((√(,9))3)

4. Evaluate the square root of 9

1/((√(,9))3)=1/3

5. Calculate the cube of 3

1/3=1/27

Final Answer

(1/9)(3/2)=1/27

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