# How do you simplify a^5/(b^3c^3) div a^4/(b^3c^4)?

Jul 27, 2015

You cancel terms common to the numerator and denominator.

#### Explanation:

Your expression can be written as

$\frac{{a}^{5}}{{b}^{3} {c}^{3}} \cdot \frac{{b}^{3} {c}^{4}}{a} ^ 4$

Use the product of powers property of exponents to rewrite the numerators of the two fractions as

${a}^{5} = {a}^{4} \cdot a$

${b}^{3} {c}^{4} = {b}^{3} {c}^{3} \cdot c$

$\frac{{a}^{4} \cdot a}{{b}^{3} {c}^{3}} \cdot \frac{{b}^{3} {c}^{3} \cdot c}{a} ^ 4$
$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{{a}^{4}}}} \cdot a}{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{{b}^{3} {c}^{3}}}}} \cdot \frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{{b}^{3} {c}^{3}}}} \cdot c}{\textcolor{red}{\cancel{\textcolor{b l a c k}{{a}^{4}}}}} = \textcolor{g r e e n}{a c}$