Evaluate (-27)^(4/3)

Problem

(−27)(4/3)

Solution

1. Rewrite the exponent using the property a(m/n)=(√(n,a))m to separate the root and the power.

(−27)(4/3)=(√(3,−27))4

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

√(3,−27)=−3

3. Substitute the result back into the expression to prepare for the final calculation.

(−3)4

4. Calculate the fourth power of −3 by multiplying (−3)×(−3)×(−3)×(−3)

(−3)4=81

Final Answer

(−27)(4/3)=81

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