Evaluate 1000^(1/3)

Problem

1000(1/3)

Solution

1. Identify the operation as finding the cube root of the number 1000 since an exponent of 1/3 is equivalent to √(3,x)

2. Rewrite the base 1000 as a power of 10 to simplify the expression.

1000=10

3. Substitute the power back into the original expression.

(10)(1/3)

4. Apply the power of a power rule, which states that (am)n=a(m⋅n)

10(3⋅1/3)

5. Simplify the exponent by multiplying the values.

3⋅1/3=1

6. Evaluate the resulting expression.

10=10

Final Answer

1000(1/3)=10

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