Simplify (a^(1/2)b)^(1/2)(ab^(1/2))

Problem

(a(1/2)*b)(1/2)*(a*b(1/2))

Solution

1. Apply the power of a product rule to the first term (a(1/2)*b)(1/2) by multiplying the outer exponent by each inner exponent.

(a(1/2⋅1/2))*(b(1/2))*(a*b(1/2))

2. Simplify the exponents in the first term.

(a(1/4)*b(1/2))*(a*b(1/2))

3. Group like bases together to prepare for multiplication.

(a(1/4)⋅a1)*(b(1/2)⋅b(1/2))

4. Apply the product rule for exponents by adding the exponents of the same bases.

a(1/4+1)*b(1/2+1/2)

5. Calculate the final exponents by performing the addition.

a(5/4)*b1

Final Answer

(a(1/2)*b)(1/2)*(a*b(1/2))=a(5/4)*b

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