Question

How do you simplify `(-2x^2y^3)(3x^4y)`?

Answer 1

You can remove all of the parentheses and rearrange terms like this:
`-2*3*x^2*x^4*y^3*y`

Explanation:

Now, multiply the numbers, and each variable that is alike:
`-6*x^6*y^4`
Make sure that you apply the Multiply-Add rule for exponents when the base is the same!
A frequently made mistake would be to multiply the exponents, or to forget that "y" is really `y^1` when adding the exponents.

Answer 2

See the entire simplification process below:

Explanation:

First step, rearrange to group like terms:

`(-2 xx 3)(x^2 xx x^4)(y^3 xx y)`

Now, combine like terms using these two rules for exponents:

`a = a^color(red)(1)`
`x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) +color(blue)(b))`

`-6(x^2 xx x^4)(y^3 xx y^1)`

`-6x^(2+4)y^(3+1)`

`-6x^6y^4`