Simplify square root of s square root of s^4

Problem

√(,s(√(,s^4())))

Solution

1. Simplify the inner radical by taking the square root of s^4()

√(,s^4())=s^2()

2. Substitute the simplified inner expression back into the original radical.

√(,s⋅s^2())

3. Combine the terms inside the radical using the product rule for exponents, s^1⋅s^2=s()^(1+2)

√(,s^3())

4. Rewrite the radical using a fractional exponent, where √(,x)=x^(1/2)

(s^3)^(1/2)

5. Apply the power rule for exponents, (a^m)^n=a^(m⋅n) to find the final simplified form.

s()^(3/2)

Final Answer

√(,s(√(,s^4())))=s()^(3/2)

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