# Simplifying Absolute Value Expressions

The absolute value of a product is the same as the product of the absolute values . For instance:

$|\text{\hspace{0.17em}}\left(9\right)\left(-3\right)\text{\hspace{0.17em}}|=|\text{\hspace{0.17em}}9\text{\hspace{0.17em}}|\text{\hspace{0.17em}}|\text{\hspace{0.17em}}-3\text{\hspace{0.17em}}|=\left(9\right)\left(3\right)=27$

$|\text{\hspace{0.17em}}\left(-11\right)\left(-10\right)\text{\hspace{0.17em}}|=|\text{\hspace{0.17em}}-11\text{\hspace{0.17em}}|\text{\hspace{0.17em}}|\text{\hspace{0.17em}}-10\text{\hspace{0.17em}}|=\left(11\right)\left(10\right)=110$

$|\text{\hspace{0.17em}}{x}^{3}y\text{\hspace{0.17em}}|=|\text{\hspace{0.17em}}{x}^{3}||y\text{\hspace{0.17em}}|$

The same goes for quotients .

$|\frac{\left(10\right)}{\left(-5\right)}|=\frac{|\text{\hspace{0.17em}}10\text{\hspace{0.17em}}|}{|\text{\hspace{0.17em}}-5\text{\hspace{0.17em}}|}=\frac{10}{5}=2$

However, the same thing doesn't always work for addition and subtraction!

$|\text{\hspace{0.17em}}-3+7\text{\hspace{0.17em}}|=|\text{\hspace{0.17em}}4\text{\hspace{0.17em}}|=4,$ but

$|\text{\hspace{0.17em}}-3\text{\hspace{0.17em}}|+|\text{\hspace{0.17em}}7\text{\hspace{0.17em}}|=3+7=10$

So be careful!