Evaluate 343^(1/3)

Problem

343^(1/3)

Solution

1. Identify the operation as finding the cube root of the number 343 since raising a number to the power of 1/3 is equivalent to √(3,x)

2. Determine if 343 is a perfect cube by testing small integers.

3. Calculate the cubes of integers: 5^3=125 6^3=216 and 7^3=343

4. Substitute the base 343 with 7^3 in the expression.

343^(1/3)=(7^3)^(1/3)

5. Apply the power of a power rule, which states (a^m)^n=a^(m⋅n)

7^(3⋅1/3)=7^1

6. Simplify the result.

7^1=7

Final Answer

343^(1/3)=7

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