Evaluate 32^(-3/5)

Problem

32(−3/5)

Solution

1. Apply the negative exponent rule by rewriting the expression as a reciprocal with a positive exponent.

32(−3/5)=1/(32(3/5))

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

1/(32(3/5))=1/((√(5,32))3)

3. Evaluate the fifth root of 32 by identifying that 2=32

√(5,32)=2

4. Substitute the root back into the expression and evaluate the power.

1/2=1/8

Final Answer

32(−3/5)=1/8

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