Evaluate 8^(-1/3)

Problem

8(−1/3)

Solution

1. Apply the negative exponent rule, which states that a(−n)=1/(an)

1/(8(1/3))

2. Rewrite the fractional exponent as a radical using the rule a(1/n)=√(n,a)

1/√(3,8)

3. Evaluate the cube root of 8 by identifying the number that, when multiplied by itself three times, equals 8

2⋅2⋅2=8

4. Substitute the value back into the expression to find the final result.

1/2

Final Answer

8(−1/3)=1/2

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