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=32

√(5,32)=2

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

1/2=1/4

Final Answer

32(−2/5)=1/4

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