Theory:

i) Division of a monomial by another monomial:
 
A monomial 40xy2 is divided by another monomial 10y will result in 40xy210y=10×4×x×y×y10×y=4xy.
 
The result of dividing a monomial by another monomial will be a monomial.
 
ii) Division of a polynomial by a monomial:
 
Divide each term of the polynomial by the monomial to get the result of the division.
 
A polynomial 12xyz3+60 is divided by a monomial 4z will result in:
 
12xyz3+604z=12xyz34z+604z.
 
=123×x×y×z×z×z4×z+604z15=3xyz2+15z
 
Dividing any polynomial by a monomial will result in a polynomial.
 
The relation between the power of exponents and division of an algebraic expression by another algebraic expression:
 
We already learnt about the power of exponents.
 
anam=anam,n>m,a0.
 
The above law of exponents can be used to divide an algebraic expression by another, for instance:
 
4xy22y=2xy21
 
=2xy
Important!
When a monomial is divided by itself, we will get \(1\).