# How do you simplify the expression (5ab^2 * 12ab)/(6ab)?

Mar 20, 2018

$10 a {b}^{2}$

#### Explanation:

$\implies \frac{5 a {b}^{2} \cdot 12 a b}{6 a b}$

Identify like-terms:

$\implies \frac{\textcolor{b l u e}{5} \textcolor{red}{a} \textcolor{\mathmr{and} a n \ge}{{b}^{2}} \cdot \textcolor{b l u e}{12} \textcolor{red}{a} \textcolor{\mathmr{and} a n \ge}{b}}{\textcolor{b l u e}{6} \textcolor{red}{a} \textcolor{\mathmr{and} a n \ge}{b}}$

Let's multiply like-terms in the numerator first:

$\implies \frac{\left(\textcolor{b l u e}{5} \cdot \textcolor{b l u e}{12}\right) \left(\textcolor{red}{a} \cdot \textcolor{red}{a}\right) \left(\textcolor{\mathmr{and} a n \ge}{{b}^{2}} \cdot \textcolor{\mathmr{and} a n \ge}{b}\right)}{\textcolor{b l u e}{6} \textcolor{red}{a} \textcolor{\mathmr{and} a n \ge}{b}}$

$\implies \frac{\textcolor{b l u e}{60} \textcolor{red}{{a}^{2}} \textcolor{\mathmr{and} a n \ge}{{b}^{3}}}{\textcolor{b l u e}{6} \textcolor{red}{a} \textcolor{\mathmr{and} a n \ge}{b}}$

Now we'll divide like-terms:

$\implies \textcolor{b l u e}{\frac{60}{6}} \textcolor{red}{{a}^{2} / a} \textcolor{\mathmr{and} a n \ge}{{b}^{3} / b}$

$\implies \textcolor{g r e e n}{10 a {b}^{2}}$

Mar 20, 2018

You must follow the rules, which include multiplying exponents as you would add, and dividing as you would subtract. Your final answer should be $10 a {b}^{2}$. This is how you do it:

#### Explanation:

$\frac{5 a {b}^{2} \cdot 12 a b}{6 a b}$
You can do this 2 different ways, by multiplying across the top first or by dividing.

By multiplying first:

$\frac{60 {a}^{2} {b}^{3}}{6 a b}$
$a \cdot a$ is ${a}^{2}$, and ${b}^{2} \cdot b$ is ${b}^{3}$, because 2+1=3.
Now divide 60 by 6, ${a}^{2}$ by $a$, and ${b}^{3}$ by $b$.
$10 a {b}^{2}$

By dividing:

$\frac{5 a {b}^{2}}{6 a b} = \frac{5 b}{6}$, as the $a$'s cancel out (1-1=0).

$\frac{5 b}{6} \cdot 12 a b = 10 a {b}^{2}$.