Evaluate fifth root of 1024

Problem

√(5,1024)

Solution

1. Identify the goal, which is to find a number that, when multiplied by itself five times, equals 1024

2. Factorize the number 1024 into its prime factors to see if it is a power of a specific integer.

3. Observe that 1024 is a well-known power of 2

1024=2⋅512

1024=2⋅2⋅256

1024=2⋅2⋅2⋅128

1024=2⋅2⋅2⋅2⋅64

1024=2⋅2⋅2⋅2⋅2⋅32

1024=2⋅32

1024=2⋅2

1024=2

4. Rewrite the expression using the exponent form of the number.

√(5,1024)=(2)1/5

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

(2)1/5=2(10⋅1/5)

6. Simplify the exponent.

2=4

Final Answer

√(5,1024)=4

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