Question 408777
Lets look at it
{{{ (9*(a^7)/(8*(b^2)))/(12*(a^2)/24*(b^7)) }}}
The RULE for simplifying SUCH a rational expression is to multiply the top 
fraction by the bottom fraction WHEN the bottom fraction is turned UPSIDE DOWN.
So we have:
{{{ ((9*(a^7))/(8*(b^2)))/(12*a^2/24*b^7) }}}={{{ (9*(a^7)/8*(b^2))*((24*(b^7))/(12*(a^2)) }}}

Now let simplify the NUMBERS.
{{{ (9*(a^7)/8*(b^2))*((24*(b^7))/(12*(a^2)) }}} = {{{ ((3*3*(a^7))/(2*2*2*(b^2)))*((2*12*(b^7))/(12*(a^2))) }}}
We cancel one group of 2's and one group of 12's and get
{{{ ((3*3*a^7)/(2*2*b^2))*((b^7)/(a^2)) }}}
{{{ ((9*a^5)/(4))*((b^5)/(1)) }}}
{{{ (9/4)*((ab)^5) }}}