# How do you simplify (10a^-8b^-2)/(4a^3b^5)?

Jun 11, 2015

 = 5/2 color(red)(a^-11b^-7

#### Explanation:

 (10a^-8b^-2)/(4a^3b^5

Note:color(red)(a^m / a^n = a^(m-n)

Applying the above property to the exponents of $a$ and $b$

$= \left(\frac{10}{4}\right) . {a}^{\textcolor{red}{\left(- 8 - 3\right)}} . {b}^{\textcolor{red}{\left(- 2 - 5\right)}}$
 = 5/2 color(red)(a^-11b^-7