How do you simplify (a^7b^5c^8)/(a^5bc^7)?

Jul 3, 2017

See a solution process below:

Explanation:

First, use this rule of exponents to rewrite the $b$ denominator:

$a = {a}^{\textcolor{red}{1}}$

$\frac{{a}^{7} {b}^{5} {c}^{8}}{{a}^{5} {b}^{\textcolor{red}{1}} {c}^{7}}$

Next, use this rule of exponents to eliminate the denominators:

${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} - \textcolor{b l u e}{b}}$

$\frac{{a}^{\textcolor{red}{7}} {b}^{\textcolor{red}{5}} {c}^{\textcolor{red}{8}}}{{a}^{\textcolor{b l u e}{5}} {b}^{\textcolor{b l u e}{1}} {c}^{\textcolor{b l u e}{7}}} = {a}^{\textcolor{red}{7} - \textcolor{b l u e}{5}} {b}^{\textcolor{red}{5} - \textcolor{b l u e}{1}} {c}^{\textcolor{red}{8} - \textcolor{b l u e}{7}} = {a}^{2} {b}^{4} {c}^{1}$

Now, use this rule of exponents to simplify the $c$ term:

${a}^{\textcolor{red}{1}} = a$

${a}^{2} {b}^{4} c$