Question

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

Answer 1

`-3(4-6)^3+(15--3)-:(1-4)=18`

Explanation:

Simplify:

`-3(4-6)^3+(15--3)-:(1-4)`

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 `(4-6)` to `color(red)(-2`.

Simplify `(15--3)` to `color(blue)18`.

Simplify `(1-4)` to `color(green)(-3`.

This simplifies to:

`-3xx(color(red)(-2))^3+color(blue)(18)-:color(green)(-3)`

Simplify the exponent.

Simplify `color(red)(-2)^3` to `color(red)(-8`. `larr` An odd number of negatives result in a negative.

`-3xxcolor(red)(-8)+color(blue)(18)-:color(green)(-3)`

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

Simplify `-3xxcolor(red)(-8)` to `color(red)(24`. `larr` 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.

`color(red)(24)color(magenta)(-6)=color(teal)18`

Answer 2

`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
Last addition and subtraction.

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

`= -3color(blue)((-2)^3 ) " "color(red)(+" "(18)div(-3))"`
`color(white)(wwwwww)darrcolor(white)(wwwwwwww)darr`
`= -3color(blue)((-8) " "color(red)(+" "(-6))`

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

`=24-6`

`=18`