Evaluate 729^(1/3)

Problem

729(1/3)

Solution

1. Identify the operation as finding the cube root of 729 since raising a number to the power of 1/3 is equivalent to √(3,x)

2. Factor the number 729 into its prime factors to see if it is a perfect cube.

729=3×243

729=3×3×81

729=3×3×3×3×3×3

3. Group the factors into three equal sets to find the cube root.

729=(3×3)×(3×3)×(3×3)

729=9×9×9

729=9

4. Apply the power rule (am)n=a(m⋅n) to simplify the expression.

(9)(1/3)=9(3⋅1/3)

9=9

Final Answer

729(1/3)=9

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