Evaluate 32^(-2/5)

Problem

32^(−2/5)

Solution

1. Apply the negative exponent rule to rewrite the expression as a reciprocal with a positive exponent.

32^(−2/5)=1/(32^(2/5))

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

1/(32^(2/5))=1/((√(5,32))^2)

3. Evaluate the fifth root of 32, noting that 2^5=32

√(5,32)=2

4. Substitute the root back into the expression and square the result.

1/2^2=1/4

Final Answer

32^(−2/5)=1/4

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