# How do you simplify (-6x^7)(-9x^12)?

##### 1 Answer
Oct 7, 2015

$54 {x}^{19}$

#### Explanation:

You need to evaluate each of the different parts of the expression separately. There are two constants and one variable with two exponents. You need to multiply the constants together to get the final constant, then multiply the $x$s together. Remember when multiplying exponents, you add them together.

$\left(- 6 {x}^{7}\right) \left(- 9 {x}^{12}\right)$
$= \left(- 6 \cdot - 9\right) {x}^{7 + 12}$
$= 54 {x}^{19}$

NOTE: You can multiply everything separately because multiplication order doesn't matter. The problem is set up as one big multiplication statement, where;

$\left(- 6 {x}^{7}\right) \left(- 9 {x}^{12}\right) = \left(- 6\right) \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot \left(- 9\right) \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x$

Multiplying the $- 9$ first simplifies this statement to;

$\left(- 6\right) \cdot \left(- 9\right) \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x$

Where you have 19 $x$s, or ${x}^{19}$.