Question

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

Answer 1

`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)`

Answer 2

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`.