Question

Simplify the problem below.

Answer 1

To solve this problem, we first must rewrite each term in the form k times a^n so that we can compute the multiplication afterwards.  To do this, we must remember that the square root of a is equivalent to a^(1/2) and that variables in the denominator have negative exponents.  Using this knowledge, we can rewrite the given expression as:

a^(1/2) * (2a² - 4a^(-1))

Now, we must recall that when terms with the same base are multiplied together, we must add the exponents when simplifying.  This step is shown below.

2a^(1/2 + 2) - 4a^(1/2 - 1)

The next step is to perform the addition of the exponents and obtain our final answer.

2a^(5/2) - 4a^(-1/2)

The above expression is your final answer.  

Hope this helps!