Evaluate (-243)^(1/5)

Problem

(−243)(1/5)

Solution

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

2. Rewrite the base −243 as a power of a prime number.

3. Recognize that 3=243 which implies that (−3)5=−243

4. Apply the property of exponents (an)m=a(n⋅m) to simplify the expression.

5. Calculate the final value by multiplying the exponents: 5⋅1/5=1

Final Answer

(−243)(1/5)=−3

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