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

Jan 21, 2017

You can remove all of the parentheses and rearrange terms like this:
$- 2 \cdot 3 \cdot {x}^{2} \cdot {x}^{4} \cdot {y}^{3} \cdot y$

Explanation:

Now, multiply the numbers, and each variable that is alike:
$- 6 \cdot {x}^{6} \cdot {y}^{4}$
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.

Jan 21, 2017

See the entire simplification process below:

Explanation:

First step, rearrange to group like terms:

$\left(- 2 \times 3\right) \left({x}^{2} \times {x}^{4}\right) \left({y}^{3} \times y\right)$

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

$a = {a}^{\textcolor{red}{1}}$
${x}^{\textcolor{red}{a}} \times {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} + \textcolor{b l u e}{b}}$

$- 6 \left({x}^{2} \times {x}^{4}\right) \left({y}^{3} \times {y}^{1}\right)$

$- 6 {x}^{2 + 4} {y}^{3 + 1}$

$- 6 {x}^{6} {y}^{4}$