Evaluate square root of 16^5

Problem

√(,16)

Solution

1. Rewrite the expression using fractional exponents to make the calculation easier.

√(,16)=(16)(1/2)

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

(16)(1/2)=16(5/2)

3. Decompose the fractional exponent into a square root and a power.

16(5/2)=(√(,16))5

4. Evaluate the square root of the base.

√(,16)=4

5. Calculate the final value by raising the result to the fifth power.

4=4⋅4⋅4⋅4⋅4

4=1024

Final Answer

√(,16)=1024

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