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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