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

2 Answers
Mar 20, 2018

10ab^2

Explanation:

We start with:

=>(5ab^2 * 12ab)/(6ab)

Identify like-terms:

=>(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:

=>((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))

=>(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:

=>color(blue)(60/6)color(red)(a^2/a)color(orange)(b^3/b)

=> color(green)(10ab^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 10ab^2. This is how you do it:

Explanation:

(5ab^2*12ab)/(6ab)
You can do this 2 different ways, by multiplying across the top first or by dividing.

By multiplying first:

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

By dividing:

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

(5b)/6*12ab=10ab^2.