# How do you simplify \frac { - 20a ^ { 3} b ^ { 8} c ^ { 4} } { 28a ^ { 3} b ^ { 7} c ^ { 5} }?

Dec 27, 2016

$- \frac{5 b}{7 c}$

#### Explanation:

There are four rules of exponents we will need to utilize in order to simplify this expression:

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

$\textcolor{b l u e}{{x}^{a} / {x}^{b} = \frac{1}{x} ^ \left(b - a\right)}$

$\textcolor{g r e e n}{{x}^{0} = 1}$

$\textcolor{p u r p \le}{{x}^{1} = x}$

Understanding these rules we can now simplify this expression as follows:

First, we can factor the constants.

$\frac{- 20 {a}^{3} {b}^{8} {c}^{4}}{28 {a}^{3} {b}^{7} {c}^{5}} \to \frac{- \left(4 \times 5\right) {a}^{3} {b}^{8} {c}^{4}}{\left(4 \times 7\right) {a}^{3} {b}^{7} {c}^{5}} \to \frac{- \left(\cancel{4} \times 5\right) {a}^{3} {b}^{8} {c}^{4}}{\left(\cancel{4} \times 7\right) {a}^{3} {b}^{7} {c}^{5}}$

$\frac{- 5 {a}^{3} {b}^{8} {c}^{4}}{7 {a}^{3} {b}^{7} {c}^{5}}$

Now, we can deal with the terms with exponents:

$\frac{- 5 \textcolor{red}{{a}^{3 - 3} {b}^{8 - 7}}}{7 \textcolor{b l u e}{{c}^{5 - 4}}} \to \frac{- 5 \textcolor{g r e e n}{{a}^{0}} \textcolor{p u r p \le}{{b}^{1}}}{7 \textcolor{p u r p \le}{{c}^{1}}} \to \frac{- 5 \times 1 \times b}{7 \times c}$

$\frac{- 5 b}{7 c}$