Evaluate (-32)^(3/5)

Problem

(−32)(3/5)

Solution

1. Rewrite the expression using the property of rational exponents a(m/n)=(√(n,a))m

(−32)(3/5)=(√(5,−32))3

2. Evaluate the fifth root of −32 by finding a number that, when multiplied by itself five times, equals −32

√(5,−32)=−2

3. Substitute the result back into the expression to prepare for the final calculation.

(−2)3

4. Calculate the cube of −2 by multiplying (−2)×(−2)×(−2)

(−2)3=−8

Final Answer

(−32)(3/5)=−8

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