how do we evaluate a fraction being raised to negative exponents ?

Try looking through this post - it will help

http://web2.0calc.com/questions/indices-especially-negative-indices

Just "flip" the fraction over and change the exponent to a positive...to see why this is so, consider......

(2/3)^-3 =  1/(2/3)³ = 1/(8/27) = (27/8)  = (3/2)³...........voila !!!!

 how do we evaluate a fraction being raised to negative exponents ?

$$\left(\dfrac{a}{b}\right)^{-n}
\\\\=
\dfrac{a^{-n}} {b^{-n}}
\\\\=
\dfrac{a^{-n}} {1}
*
\dfrac{1} {b^{-n}}
\\\\=
\dfrac{1} {a^n}
*
\dfrac{b^n } {1}
\\\\=
\dfrac{b^n} {a^n}
\\\\=
\left(\dfrac{b}{a}\right)^n
\\\\
\boxed{\left(\dfrac{a}{b}\right)^{-n}=\left(\dfrac{b}{a}\right)^n }$$