Andrew,
Simplifying this variable expression is very much like simplifying the fraction ^{810}/_{225} . With this fraction I would probably first notice that 5 divides both the numerator and denominator, so dividing both by 5 I get
^{810}/_{225} = ^{162}/_{45}
Now I notice that 9 divides both the numerator and denominator, so dividing both by 9 I get
^{810}/_{225} = ^{162}/_{45} = ^{18}/_{5}
There are no further common factors in the numerator and denominator so my answer is
^{810}/_{225} = ^{18}/_{5}
The technique is similar with 3g^{2}h over 12gh. First I notice that there is a common factor of h in the numerator and denominator. Hence
^{3g2h}/_{12gh} = ^{3g2}/_{12g}
Next there is a g common factor in the numerator and denominator so
^{3g2h}/_{12gh} = ^{3g2}/_{12g} = ^{3g}/_{12}
Finally 3 divides both the numerator and denominator so
^{3g2h}/_{12gh} = ^{3g2}/_{12g} = ^{3g}/_{12} = ^{g}/_{4}
Penny
