Evaluate seventh root of 128

Problem

√(7,128)

Solution

1. Identify the number inside the radical and the index of the root. We are looking for a number x such that x7=128

2. Factor the number 128 into its prime factors to see if it can be expressed as a power of 7

3. Calculate the powers of small integers.

2=2

2=4

2=8

2=16

2=32

2=64

2=128

4. Substitute the exponential form back into the radical expression.

√(7,2)

5. Simplify the expression by applying the rule √(n,an)=a for positive a

2

Final Answer

√(7,128)=2

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