How do you simplify the expression $\frac{5 a b^{2} \cdot 12 a b}{6 a b}$ $(5ab^2 * 12ab)/(6ab)$ ?

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How do you simplify the expression $\frac{5 a b^{2} \cdot 12 a b}{6 a b}$ $(5ab^2 * 12ab)/(6ab)$ ?

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Answer 1 · 2018-03-20T02:30:21

$10 a b^{2}$ $10ab^2$

Explanation:

We start with:

$\Rightarrow \frac{5 a b^{2} \cdot 12 a b}{6 a b}$ $=>(5ab^2 * 12ab)/(6ab)$

Identify like-terms:

$\Rightarrow \frac{5 a b^{2} \cdot 12 a b}{6 a b}$ $=>(color(blue)(5)color(red)(a)color(orange)(b^2) * color(blue)(12)color(red)(a)color(orange)(b))/(color(blue)(6)color(red)(a)color(orange)(b))$

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

$\Rightarrow \frac{(5 \cdot 12) (a \cdot a) (b^{2} \cdot b)}{6 a b}$ $=>((color(blue)(5)*color(blue)(12))(color(red)(a)*color(red)(a))(color(orange)(b^2)*color(orange)(b)))/(color(blue)(6)color(red)(a)color(orange)(b))$

$\Rightarrow \frac{60 a^{2} b^{3}}{6 a b}$ $=>(color(blue)(60)color(red)(a^2)color(orange)(b^3))/(color(blue)(6)color(red)(a)color(orange)(b))$

Now we'll divide like-terms:

$\Rightarrow \frac{60}{6} \frac{a^{2}}{a} \frac{b^{3}}{b}$ $=>color(blue)(60/6)color(red)(a^2/a)color(orange)(b^3/b)$

$\Rightarrow 10 a b^{2}$ $=> color(green)(10ab^2)$

Answer 2 · 2018-03-20T02:50:14

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

Explanation:

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

By multiplying first:

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

By dividing:

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

$\frac{5 b}{6} \cdot 12 a b = 10 a b^{2}$ $(5b)/6*12ab=10ab^2$ .

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How do you simplify the expression $\frac{5 a b^{2} \cdot 12 a b}{6 a b}$ $(5ab^2 * 12ab)/(6ab)$ ?

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Explanation:

Explanation:

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How do you simplify the expression $\frac{5 a b^{2} \cdot 12 a b}{6 a b}$ $(5ab^2 * 12ab)/(6ab)$ ?