Question 862109
Both exponents start as negative; and there is a rule like, {{{b^(-a)=1/b^a}}}.
Not really the best rule to most immediately use.  Notice both bases are 27.  Also is the exponent rule like {{{(b^a)/b^c=b^(a-c)}}}, more useful here.

{{{27^(-2/3)/27^(-1/3)}}}

{{{27^(-2/3-(-1/3))}}}

{{{27^(1/3-2/3)}}}

{{{27^(-1/3)}}}

and NOW you can use the first stated rule about the negative exponents:

WAIT.  Not really necessary.  WHY?  


{{{(3^3)^(-1/3)}}}, simply factored the base;

Know THIS rule:  {{{(b^a)^c=b^(ac)}}}


Next step then is
{{{3^(3(-1/3))}}}

{{{3^(-1)}}}

{{{highlight((1/3))}}}


One big problem on the site is that rendering of rational exponents often works badly.  write me a message if you want to see the steps through a different form or platform.