Evaluate (-32)^(1/5)

Problem

(−32)^(1/5)

Solution

1. Identify the operation as finding the fifth root of a negative number.

2. Rewrite the base −32 as a power of a prime number, noting that 2^5=32

3. Express the negative base using the property that (−a)^n=−a^n for odd exponents n

(−32)^(1/5)=((−2)^5)^(1/5)

4. Apply the power of a power rule (a^m)^n=a^(m⋅n) to simplify the exponent.

5⋅1/5=1

5. Simplify the expression to find the final value.

(−2)^1=−2

Final Answer

(−32)^(1/5)=−2

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