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 3^5=243 which implies that (−3)^5=−243

4. Apply the property of exponents (a^n)^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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