Evaluate (-243)^(3/5)

Problem

(−243)(3/5)

Solution

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

(−243)(3/5)=(√(5,−243))3

2. Identify the fifth root of −243 by finding a number that, when multiplied by itself five times, equals −243

(−3)5=−243

3. Substitute the value of the fifth root back into the expression.

√(5,−243)=−3

(−3)3

4. Evaluate the cube of −3

−3⋅−3⋅−3=−27

Final Answer

(−243)(3/5)=−27

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