Evaluate (-8)^(4/3)

Problem

(−8)(4/3)

Solution

1. Rewrite the rational exponent as a power of a root using the property a(m/n)=(√(n,a))m

(−8)(4/3)=(√(3,−8))4

2. Evaluate the cube root of −8 which is the number that, when multiplied by itself three times, equals −8

√(3,−8)=−2

3. Substitute the result back into the expression and raise it to the fourth power.

(−2)4=(−2)⋅(−2)⋅(−2)⋅(−2)

4. Calculate the final value by performing the multiplication.

(−2)4=16

Final Answer

(−8)(4/3)=16

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