Evaluate 512^(1/3)

Problem

512(1/3)

Solution

1. Identify the operation as finding the cube root of the number 512, since raising a number to the power of 1/3 is equivalent to √(3,512)

2. Determine the prime factorization of 512 to find a number that, when multiplied by itself three times, equals 512.

3. Factor the number 512 into powers of 2.

512=2

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

(2)(1/3)=2(9⋅1/3)

5. Simplify the exponent by performing the multiplication.

2=8

Final Answer

512(1/3)=8

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