Evaluate (-64)^(4/3)

Problem

(−64)(4/3)

Solution

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

(−64)(4/3)=(√(3,−64))4

2. Evaluate the cube root of −64 by finding a number that, when multiplied by itself three times, equals −64

√(3,−64)=−4

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

(−4)4

4. Calculate the fourth power of −4 noting that a negative number raised to an even power results in a positive value.

(−4)×(−4)×(−4)×(−4)=256

Final Answer

(−64)(4/3)=256

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