# 1.9 Division of Algebraic Expressions

**Dividing Monomials • Dividing by a Monomial • Dividing One Polynomial by Another**

To find the quotient of one monomial divided by another, we use the laws of exponents and the laws for dividing signed numbers. Again, the *exponents may be combined only if the base is the same*.

# EXAMPLE 1 Dividing monomials

$\frac{{\displaystyle 3{c}^{7}}}{{\displaystyle {c}^{2}}}\hspace{0.17em}=\hspace{0.17em}3{c}^{7\hspace{0.17em}-\hspace{0.17em}2}\hspace{0.17em}=\hspace{0.17em}3{c}^{5}$

$\frac{{\displaystyle \hspace{0.17em}-\hspace{0.17em}6{a}^{2}x{y}^{2}}}{{\displaystyle 2ax{y}^{4}}}\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}\left(\frac{6}{2}\right)\text{}\frac{{\displaystyle {a}^{2\hspace{0.17em}-\hspace{0.17em}1}{x}^{1\hspace{0.17em}-\hspace{0.17em}1}}}{{\displaystyle {y}^{4\hspace{0.17em}-\hspace{0.17em}2}}}\hspace{0.17em}=\hspace{0.17em}\frac{{\displaystyle \hspace{0.17em}-\hspace{0.17em}3a}}{{\displaystyle {y}^{2}}}$

As shown in illustration (c), we use only positive exponents in the final result unless there are specific instructions otherwise.

From arithmetic, we may show how a multinomial is to be divided by ...

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