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

Problem

(1/25)3/2

Solution

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

(1/25)3/2=1/25

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

1/25

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

1/((√(,25))3)

4. Evaluate the square root of 25.

1/5

5. Calculate the cube of 5 to find the final value.

1/125

Final Answer

(1/25)3/2=1/125

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