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

Want more problems? Check here!