Evaluate 8^(1/3)

Problem

8(1/3)

Solution

1. Identify the meaning of the fractional exponent, where an exponent of 1/3 represents the cube root of the base.

8(1/3)=√(3,8)

2. Rewrite the base as a power of a prime number, noting that 8 can be expressed as 2 raised to the third power.

8=2

3. Substitute the power back into the expression and apply the power of a power rule, which states (am)n=a(m⋅n)

(2)(1/3)=2(3⋅1/3)

4. Simplify the exponent by multiplying the values.

3⋅1/3=1

5. Calculate the final value.

2=2

Final Answer

8(1/3)=2

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