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

2 Answers
Dec 31, 2017

Answer:

#-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#

Mar 1, 2018

Answer:

#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#