Simplify square root of 121(z-2)^14

Problem

√(,121*(z−2)14)

Solution

1. Apply the product property of radicals to separate the constant and the variable expression.

√(,121⋅(z−2)14)=√(,121)⋅√(,(z−2)14)

2. Evaluate the square root of the constant coefficient.

√(,121)=11

3. Apply the power rule for radicals which states that √(,xn)=|x|(n/2) for even roots.

√(,(z−2)14)=|z−2|(14/2)

4. Simplify the exponent by dividing 14 by 2.

|z−2|(14/2)=|*z−2|7

5. Combine the results into a single expression.

11⋅|z−2|7

Final Answer

√(,121*(z−2)14)=11|z−2|7

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