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 x^m⋅x^n=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.

a^2−2*a^1

Final Answer

a^(1/2)*(a^(3/2)−2*a^(1/2))=a^2−2*a

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