# How do you simplify -3( 4- 6) ^ { 3} + ( 15- - 3) \div ( 1- 4)?

Dec 31, 2017

$- 3 {\left(4 - 6\right)}^{3} + \left(15 - - 3\right) \div \left(1 - 4\right) = 18$

#### Explanation:

Simplify:

$- 3 {\left(4 - 6\right)}^{3} + \left(15 - - 3\right) \div \left(1 - 4\right)$

You will need to follow the order of operations:

Parentheses/brackets
Exponents/Powers
Multiplication and division in order from left to right.
Addition and subtraction in order from left to right.

Simplify the parentheses.

Simplify $\left(4 - 6\right)$ to color(red)(-2.

Simplify $\left(15 - - 3\right)$ to $\textcolor{b l u e}{18}$.

Simplify $\left(1 - 4\right)$ to color(green)(-3.

This simplifies to:

$- 3 \times {\left(\textcolor{red}{- 2}\right)}^{3} + \textcolor{b l u e}{18} \div \textcolor{g r e e n}{- 3}$

Simplify the exponent.

Simplify ${\textcolor{red}{- 2}}^{3}$ to color(red)(-8. $\leftarrow$ An odd number of negatives result in a negative.

$- 3 \times \textcolor{red}{- 8} + \textcolor{b l u e}{18} \div \textcolor{g r e e n}{- 3}$

Multiply. (Do this before the division because it is first in the expression.)

Simplify $- 3 \times \textcolor{red}{- 8}$ to color(red)(24. $\leftarrow$ Two negatives result in a positive.

color(red)(24)+color(blue)(18)-:color(green)(-3

Divide. (Do this after the multiplication because it comes later in the expression.

Simplify color(blue)(18)-:color(green)(-3 to color(magenta)(-6.

color(red)(24)color(magenta)(-6

Subtract.

$\textcolor{red}{24} \textcolor{m a \ge n t a}{- 6} = \textcolor{t e a l}{18}$

Mar 1, 2018

$18$

#### Explanation:

There are several different operations to be done.

Count the number of terms first. Each must be simplified to a single answer which can be added or subtracted in the last step.

There are two terms:

color(blue)(-3(4-6)^3)" " color(red)(+" "(15--3)div(1-4))

Within each term you have to do what is inside the brackets first:
Then any powers
Then multiplication and division

= -3(color(blue)(-2))^3 " "color(red)(+" "(15+3)div(-3))

$= - 3 \textcolor{b l u e}{{\left(- 2\right)}^{3}} \text{ "color(red)(+" "(18)div(-3))}$
$\textcolor{w h i t e}{w w w w w w} \downarrow \textcolor{w h i t e}{w w w w w w w w} \downarrow$
$= - 3 \textcolor{b l u e}{\left(- 8\right) \text{ "color(red)(+" } \left(- 6\right)}$

= color(blue)(+24 " "color(red)(+" "(-6)

$= 24 - 6$

$= 18$