3.

(6x^2y^5)/(9x^4y^3)

 

One way to develop an appreciation for exponents is to write the problem without using them. Break the coefficients up into products of primes and spread out the variables.

 

((3x+4)(3x-4))/((3x-4)(3x-4))

 

When we cancel the factors that survive are

 

(3x+4)/(3x-4)

 

This illustrates the rules for dealing with exponents. When dividing powers of the same base we subtract the exponents. In this case when we take away the 4 factors of x in the bottom from the 2 factors of x in the top we ate left with negative 2 factors or 2 factors in the bottom. With the y's when we take the 3 factors in the bottom away from the 5 factors in the top, we are left with 2 factors in the top.