Simplify a^(1/2)(a^(3/2)-2a^(1/2))

Problem

a(1/2)*(a(3/2)−2*a(1/2))

Solution

1. Distribute the term a(1/2) to each term inside the parentheses.

a(1/2)⋅a(3/2)−a(1/2)⋅2*a(1/2)

2. Apply the product rule for exponents, which states that xm⋅xn=x(m+n) to the first term.

a(1/2+3/2)−2*a(1/2+1/2)

3. Simplify the exponents by adding the fractions.

a(4/2)−2*a(2/2)

4. Reduce the fractions in the exponents to their simplest form.

a2−2*a1

Final Answer

a(1/2)*(a(3/2)−2*a(1/2))=a2−2*a

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