# How do you evaluate (2x ^ { 5} ) ( - 3x ^ { 9} ) ( 9x ^ { 9} )?

Nov 29, 2017

you should be able to do it in your head - it's not difficult:

#### Explanation:

1. Multiply the constants 2, -3, and 9. (-54)

2. Multiply the powers of 'x' terms, by writing x, raised to a power equal to the SUM of the powers of the original terms.

This is ${x}^{5 + 9 + 9} = {x}^{23}$

1. Put it all together:

$- 54 {x}^{23}$

GOOD LUCK

Nov 29, 2017

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$\left(2 \times - 3 \times 9\right) \left({x}^{5} \times {x}^{9} \times {x}^{9}\right) \implies$

$- 54 \left({x}^{5} \times {x}^{9} \times {x}^{9}\right)$

Now, use this rule for exponents to multiply the $x$ terms:

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

$- 54 \left({x}^{\textcolor{red}{5}} \times {x}^{\textcolor{b l u e}{9}} \times {x}^{\textcolor{g r e e n}{9}}\right) \implies$

$- 54 {x}^{\textcolor{red}{5} + \textcolor{b l u e}{9} + \textcolor{g r e e n}{9}} \implies$

$- 54 {x}^{23}$