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**i) Division of a monomial by another monomial**:

A monomial $40x{y}^{2}$ is divided by another monomial $10y$ will result in $\frac{40x{y}^{2}}{10y}=\frac{\overline{)10}\times 4\times x\times y\times \overline{)y}}{\overline{)10}\times \overline{)y}}=4\mathit{xy}$.

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 $-12\mathit{xy}{z}^{3}+60$ is divided by a monomial $4z$ will result in:

$\frac{-12\mathit{xy}{z}^{3}+60}{4z}=\frac{-12\mathit{xy}{z}^{3}}{4z}+\frac{60}{4z}$.

$\begin{array}{l}=\frac{{\overline{)-12}}^{-3}\times x\times y\times z\times z\times \overline{)z}}{\overline{)4}\times \overline{)z}}+{\frac{\overline{)60}}{\overline{)4}z}}^{15}\\ \\ =-3\mathit{xy}{z}^{2}+\frac{15}{z}\end{array}$

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.

$\frac{{a}^{n}}{{a}^{m}}={a}^{n}-{a}^{m},n>m,a\ne 0.$

The above law of exponents can be used to divide an algebraic expression by another, for instance:

$\frac{4x{y}^{2}}{2y}=2x{y}^{2-1}$

$=2\mathit{xy}$

Important!

When a monomial is divided by itself, we will get \(1\).