Evaluate (-27)^(2/3)

Problem

(−27)(2/3)

Solution

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

(−27)(2/3)=(√(3,−27))2

2. Evaluate the cube root of −27 by finding a number that, when multiplied by itself three times, equals −27

√(3,−27)=−3

3. Substitute the result back into the expression and square it.

(−3)2=9

Final Answer

(−27)(2/3)=9

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