# How do you simplify (-5abc^4)(-3a^3c^2)(-4a^2b^4c^3)?

Jan 6, 2017

To solve this problem, you have to seperate the numbers from the variables and then multiply.

#### Explanation:

This problem may seem complicated. However, everything becomes clear when you seperate out the numbers and the variables. Simply put, you can use the Commutative Property of Multiplication to rearrange the factors in this problem to make it less mind-boggling.

Let's take a look at the problem again. The problem is telling you to evaluate the following mathematical expression:

$\left(- 5 a b {c}^{4}\right) \left(- 3 {a}^{3} {c}^{2}\right) \left(- 4 {a}^{2} {b}^{4} {c}^{3}\right)$

Using the Commutative Property of Multiplication, we can rearrange the factors of this expression in anyway we want because it won't change the final result. So, utilizing this property, we can rearrange it like this so that all the numbers are on the left hand side and all the variables and powers are on the right side:

$\left(- 5\right) \left(- 3\right) \left(- 4\right) \left(a\right) \left({a}^{3}\right) \left({a}^{2}\right) \left(b\right) \left({b}^{4}\right) \left({c}^{4}\right) \left({c}^{2}\right) \left({c}^{3}\right)$

Now, we can simplify the expression:

$\left(- 60\right) \left({a}^{6}\right) \left({b}^{5}\right) \left({c}^{9}\right)$

And now, we can merge everything together, revealing the answer:

$- 60 {a}^{6} {b}^{5} {c}^{9}$