[tex](25)^{-\frac{1}{2} }[/tex]
When the exponent is negative, you have to make the number a fraction(1 over the number).
For example:
[tex]25^{-2} = \frac{1}{25^{2} }[/tex]
[tex]x^{-1} =\frac{1}{x^{1} }[/tex]
This gets rid of the negative, but it leaves the exponent
[tex](25)^{-\frac{1}{2}} = \frac{1}{25^{1/2}}[/tex]
When an exponent is a fraction, it is the square root.
For example:
[tex]x^{\frac{1}{3}} = \sqrt[3]{x}[/tex]
[tex]x^{\frac{1}{2}} =\sqrt{x}[/tex]
[tex]x^{\frac{1}{4}}=\sqrt[4]{x}[/tex]
So...
[tex]\frac{1}{25^{1/2}} = \frac{1}{\sqrt{25} } = \frac{1}{5}[/tex]
