Evaluate 8^(-4/3)

Problem

8(−4/3)

Solution

1. Apply the negative exponent rule by rewriting the expression as a reciprocal with a positive exponent.

8(−4/3)=1/(8(4/3))

2. Interpret the rational exponent using the rule a(m/n)=(√(n,a))m which means taking the cube root of the base first.

1/(8(4/3))=1/((√(3,8))4)

3. Evaluate the cube root of the base number 8

√(3,8)=2

4. Substitute the root back into the expression and apply the remaining power.

1/2

5. Calculate the final value by raising 2 to the power of 4

2=16

Final Answer

8(−4/3)=1/16

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