Step-by-step explanation:
First of all, [tex]\frac{-1}{-2}[/tex] is equal to [tex]\frac{1}{2}[/tex] because a negative divided by a negative is positive. So now we've got [tex]2a^\frac{1}{2}[/tex]. Well, a fractional exponent, when simplified, is a root. For example, [tex]x^\frac{1}{3}[/tex] is equal to [tex]\sqrt[3]{x}[/tex], and [tex]x^\frac{2}{5}[/tex] is equal to [tex]\sqrt[5]{x^2}[/tex].
Now this is where people make mistakes. Remember, [tex]2a^\frac{1}{2}[/tex] is really [tex]2*a^\frac{1}{2}[/tex], which means only a is raised to the exponent. We would only raise 2a to the power of [tex]\frac{1}{2}[/tex] if our term was [tex](2a)^\frac{1}{2}[/tex]. But since our term is [tex]2*a^\frac{1}{2}[/tex] we raise a to the power of [tex]\frac{1}{2}[/tex] which is the same as [tex]\sqrt[2]{a}[/tex] or just [tex]\sqrt{a}[/tex]. Then we multiply that result by 2 and we have [tex]2\sqrt{a}[/tex] which is fully simplified.
