How do you simplify #[96+ ( - 4) ] ^ { 3} - 11\cdot 10#?

2 Answers
Mar 13, 2018

Use PEMDAS to reduce the expression down to a single number... which in this case is 778578

Explanation:

PEMDAS is an acronym that stands for:
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction

And is the correct order of operations when doing Arithmetic. For this expression, we will start with the First set of Parentheses:

#[96+(-4)]#

There's another set of parentheses here, which we will expand. We know that adding a negative number is the same as subtracting it, so we can change the above to:

#[96-4]=[92]#

This changes our expression to:

#92^3-11*10#

The next step in PEMDAS is Exponents. The first term here is raised to the 3rd power:

#92^3=92*92*92=778688#

Our expression now looks like this:

#778688-11*10#

The next step in PEMDAS is Multiplication. There is one multiplication in this equation:

#11*10=110#

Our equation is now:

#778688-110#

There is no Division or Addition, so those steps can be skipped. The last step is to Subtract.

#778688-110=color(red)(778578#

Mar 13, 2018

#778,578#

Explanation:

Count the number of terms first.
Terms are separated by #+ and -# signs.

Each term simplifies to a single answer and they are then added or subtracted in the last step.

Within each term work from inner brackets outwards and do the stronger operations of powers and roots before multiplication and division.

In this expression there are two terms.

#color(blue)([96+(-4)]^3) color(purple)(" " -" "11 xx10)#

#=color(blue)([96-4]^3) color(purple)(" " -" "110)#

#=" "color(blue)([92]^3) color(purple)(" " -" "110)#

#=" "color(blue)(778,688) color(purple)(" " -" "110)#

#=" "778,578#