Evaluate (-64)^(2/3)

Problem

(−64)^(2/3)

Solution

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

(−64)^(2/3)=(√(3,−64))^2

2. Evaluate the cube root of −64 Since (−4)×(−4)×(−4)=−64 the cube root is −4

√(3,−64)=−4

3. Square the result obtained from the cube root.

(−4)^2=16

Final Answer

(−64)^(2/3)=16

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