Evaluate (-216)^(2/3)

Problem

(−216)(2/3)

Solution

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

(−216)(2/3)=(√(3,−216))2

2. Evaluate the cube root of the base. Since (−6)⋅(−6)⋅(−6)=−216 the cube root of −216 is −6

√(3,−216)=−6

3. Square the result obtained from the cube root.

(−6)2=36

Final Answer

(−216)(2/3)=36

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