For this case we have, by definition:
[tex]a^{-b} =\frac{1}{a ^ b}[/tex]
So, we have:
[tex]\frac{1}{4}^{-\frac{1}{2}}=\frac{1}{(\frac{1}{4})^{\frac{1}{2}}}[/tex]
On the other hand we have that by definition:
[tex]a^{\frac{1}{2}}=\sqrt{a}[/tex]
Thus, the expression can be written as:
[tex]\frac{1}{\sqrt {\frac{1}{4}}} =[/tex]
[tex]\frac{1}{\frac{1}{\sqrt{4}}}[/tex]
[tex]\frac{1}{\frac{1}{2}}[/tex]
[tex]\frac{1*2}{1*1}=2[/tex]
So, we have:
[tex]\frac{1}{4}^{-\frac{1}{2}}= 2[/tex]
Answer:
[tex]\frac{1}{4}^{-\frac{1}{2}}= 2[/tex]
